How to factor a tri, quad, or polynomial.

Answers

Answer 1

Explanation:

Factoring to linear factors generally involves finding the roots of the polynomial.

The two rules that are taught in Algebra courses for finding real roots of polynomials are ...

Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)

In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.

Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)

__

Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.

There are web apps that will find all roots of virtually any polynomial of interest.

_____

Additional comment

Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.


Related Questions

what is x^2+6^2=10^2

Answers

Answer:

Follow the order of operations and then solve from there

x^2 is simplifed to its max

6^2 is 36

10^2 is 100

x^2+36=100

Follow it normally

x^2=64

√64 = 8

x=8

**edited, sorry for the incorrect answer**

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

First lets write our equation

[tex]x^2+6^2=10^2[/tex]

Solve

We will use PEMDAS, or also known as BOMDAS

[tex]x^2+36=100[/tex]

Subtract 36 from both sides

[tex]x^2=64[/tex]

Find the square root of 64

[tex]\sqrt{64} =8[/tex]

[tex]x=8[/tex]

Brainliest please :)

−2p + 23 = 15

What does p =

Answers

Answer:

look at the picture .................

what is the sum of the first 8 terms of the geometric sequence 1, 1/2,1/4,1/8,..

(with solution)

PA HELP PO THANKYOUU~

Answers

Answer:

127/64  

Step-by-step explanation:  

1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64  

add all the given and it will result to 127/64

Graph 4x + 7y ≤ 28 in the first quadrant of the coordinate plane.

Answers

Answer:

StGraph the line using the slope and y-intercept, or two points.

Slope: −47

y-intercept: (0,−4)

x     y

−7    0

0    −4

Step-by-step explanation:

PLEASE HELP I DONT UNDSRSTANT

Answers

Answer:

  B.  28.5

Step-by-step explanation:

Before you can use the Law of Sines, you need to know the measure of angle C. The sum of angles in a triangle is 180°, so you have ...

  A + B + C = 180°

  C = 180° -A -B = 180° -32° -25° = 123°

The Law of Sines tells you ...

  c/sin(C) = a/sin(A)

  c = sin(C)·a/sin(A) = sin(123°)·18/sin(32°)

  c ≈ 28.5

_____

Additional comment

The law of sines says the ratio of a side length to the sine of the opposite angle is a constant for any given triangle:

  a/sin(A) = b/sin(B) = c/sin(C)

In order to use this relationship, you need to have a side length and its opposite angle. If you're solving for a side length, as here, you need to know the angle opposite that side.

This problem gives you side 'a' and angle A, and it asks for side 'c'. That means you need to know angle C, which we found as part of our solution.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.The measure of angle ABC is °.The measure of angle BAC is °.The measure of angle ACB is °.

Answers

Answer:

Angle B is the linear pairs with 60°, so the size is 180-60=120°

Angle ABC is the linear pair with 120°, so the size is 180-120-60°

Angle A corresponds to angle 60°, so they are equal

Angle BAC is the linear pair with angle A and angle 70°, so 180-(60+70)=50°

Angle ACB is 180-(50+60) = 70°

Step-by-step explanation:

The solution is:

The measure of angle ABC is 60°.

The measure of angle BAC is 50°.

The measure of angle ACB is 70°.

What is an angle?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Angle B is the linear pairs with 60°,

so the size is 180-60=120°

Angle ABC is the linear pair with 120°,

so the size is 180-120 =60°

Angle A corresponds to angle 60°,

so they are equal

Angle BAC is the linear pair with angle A and angle 70°,

so 180-(60+70) =50°

and, we have,

Angle ACB is 180-(50+60) = 70°

Hence, The solution is:

The measure of angle ABC is 60°.

The measure of angle BAC is 50°.

The measure of angle ACB is 70°.

To learn more on angle click:

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#SPJ7

What equation represents this sentence?

28 is the quotient of a number and 4.


28=n4

4=n28

4=28n

28=4n

Answers

I think it’s 28=4n because quotient means the result of. And then I get 4n because the number comes before the variable.

The equation represents this sentence"28 is the quotient of a number and 4" will be n/4=28.

What is an equation?

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation. The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero.

It is given that, 28 is the quotient of a number and 4.

The number being divided is referred to as the dividend, and the number being divided by it is referred to as the divisor. The quotient is the outcome of the division.

Suppose the number is n,

n/4=28

Thus, the equation represents this sentence"28 is the quotient of a number, and 4" will be n/4=28.

Learn more about the equation here,

https://brainly.com/question/10413253

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can someone please help me with this

Answers

Answer:

y-intercept =3

x-intercept =3/2

slope =-2

Step-by-step explanation:

y=-2x+3

0=-2x+3

2x=3

x=3/2

A right triangle has an X exterior angle with a measure of 142° . Can you determine the measures of the interior angles? Explain.

Answers

Answer: The interior angles are 38, 52, 90

=======================================================

Explanation:

The exterior angle of 142 leads to an interior angle of 180-142 = 38. The adjacent interior/exterior pair of angles always add to 180. So 38+142 = 180. These two angles are supplementary, which is another way of saying they form a straight line.

Since 38 is one of the acute interior angles, the other acute interior angle is 90-38 = 52. The rule is that the acute interior angles of any right triangle always add to 90 degrees (i.e. the angles are complementary).

Lastly, the remaining interior angle is the 90 degree angle itself. All right triangles have exactly one angle that is 90 degrees. The term "right angle" is often used in place of "90 degree angle".

The population mean for a college Introduction to Biology quiz is 15 points. A sample of 45 high school seniors earns an average of 18.54 points. A 90% confidence interval for the true mean of high school seniors is [15.87, 21.20]. Based on this confidence interval, what would your decision be in regard to a 2-tailed null with an alpha level of 0.1

Answers

Answer:

C) Reject null, because 15 is not in the interval.

Step-by-step explanation:

Arron and Paul are paid 10$ per hour as landscapers. However this week Arron made an additional 54$ in overtime pay. Given that A and P represent the number of hours worked by Arron (a) and Paul (p) which expresion can be used to represent their combined earrings for the week.


A. 10A+10P+54
B. 10AP+54
C. 10P+54
D. 10A(54)+10P

Answers

D. 10A(54)+10P

Is the correct answer

Answer:

A. 10A+10P+54

Step-by-step explanation:

Carlos bought a new cell phone. The graph represents the
relationship between the number of minutes he uses
and the total
cost. What is the equation of the line?

A) y= 5x + 0.1
B) y=0.1x + 5
C) y=0.5x + 5
D) y = 5x + 5

Answers

Answer:

B : y = 0.1x + 5

Step-by-step explanation:

using the y = mx + b equation

b is the intercept on the y axis ( x = 0)

m is the slope of the line.

From the graph we can see that the intercept is (0,5), therefore b = 5;

To calculate slope (m) pick two pints on the line e.g (100, 15) and (0, 5)

m = (y2 - y1)/(x2 -x1) = (15 - 5)/(100 - 0) = 10/100 = 0.1

m = 0.1

therefore in y = mx + b

y = 0.1x + 5

Which visual fraction model correctly shows the shaded region for the expression 1/2 divided by 6?

Answers

Answer: C

Step-by-step explanation: half of 6 is 3 so its C

YAll plssssss help me with 5 plsssssssss

Answers

Answer:

8 and 2

Step-by-step explanation:

If you add them together you get 10. (8 + 2 = 10)

If you multiply them you get 16. (8 x 2 = 16)

Have a great day! (I'd love brainiest if you could give it to me!)

A fabric store is having a sale. Fleece fabric has an original price of $18 per yard. It is on sale for 30% off the original price. Find the sale price of the fleece fabric.

I seriously needed answers since I'm running out of time​

Answers

Answer:the answer is 5.4

Step-by-step explanation:

thats the answer because it says per means to multiply so i'd multipled 18x 30%

What is the slope for this table?

Answers

Answer:

look at the picture ..........

someone pls help it’s due today :(

Answers

180 - 28 - 14 = 138

so 12x - 18 = 138

x = 13

Find the perimeter. Simplify the answer

Answers

Answer:

Perimeter = 16c + 24

Step-by-step explanation:

Perimeter = 4c + 7 + 4c + 7 + 8c + 10

Perimeter = 16c + 14 + 10

Perimeter = 16c + 24

-Chetan K

16c + 24

Step-by-step explanation:

To Find the perimeter we add

all the sides,

= > 4c + 7 + 4c + 7 + 8c + 10

= > 16c + 24...ans

Hope it Helps you!!

Solve the conjunctions below.

2 < x/3 - 5 < 6

3 < 2(x + 2) - 7 ≤ 13

Answers

Answer:

top: 21 < x < 33

bottom: 3 < x ≤ 8

Step-by-step explanation:

12×6×2+10×6×2+12×10×2​

Answers

Answer:

504

Step-by-step explanation:

The answer is 504.

Thank me later

Renata moved to her new home a few years ago. Back then, the young oak tree in her back yard was 190 centimeters tall. She measured it once a year and found that it grew at a constant rate. 3 years after she moved into the house, the tree was 274 centimeters tall
How fast did the tree grow?

How many years passed from the time Renata moved in until the tree was 344 centimeters tall?

Answers

1.

The equation for this problem would be

y = (?)x + 190

With y being the height after a given amount of years and x being the amount of years passing. We would need to find ?, the rate of how fast the tree grows. The problem gives us y = 274 centimeters and x = 3 years

Let’s plug in and solve for ?

274 = ?(3) + 190

84 = ?3

28 = ?

The tree grew 28 cm per year

2.

Since we know the rate of change and y, let’s just plug in values

344 = 28x + 190

154 = 28x

5.5 = x

5.5 years since Renata moved.

Answer:

Answers below

Step-by-step explanation:

How fast did the tree grow?

28 centimeters per year

How many years passed from the time Renata moved in until the tree was 344 centimeters tall?

5.5 years

Hope this helps!

I just woke up i need help ;-;

Answers

Answer:

i think that the correct answer is 7/12

Mark has 2,250 t-shirts to sell. He sold 25% of the
shirts on Monday, 45% on Tuesday and the rest on
Wednesday. How many shirts did he sell on
Wednesday?

Answers

Answer:

1575

Step-by-step explanation:

solve for x in the triangle

Answers

Answer:

x=9

Step-by-step explanation:

Since the sides are the same, the base angles must be the same

8x+2 = 10x-16

Subtract 8x from each side

8x+2-8x =10x-16-8x

2 = 2x-16

Add 16 to each side

2+16 = 2x-16+16

18 =2x

Divide by 2

18/2 =2x/2

9 =x

can you help me please

Answers

Answer:

i cant read that

Step-by-step explanation:

By VCR Sales A dealer carries two models of VCRs. One sells for
$300 and the other sells for $225. The dealer sells 22 VCRs for a
total revenue of $5700. How many of each type did the dealer sell?

Answers

Answer:

2333

Step-by-step explanation:

This recipe makes 8 pancakes.
Sanjay follows the recipe but wants to make 24 pancakes.
How much of each ingredient does he need?

Recipe: Makes 8
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 mL milk
1 egg
2 tablespoons (tbsps) oil

Answers

Answer:

If Sanjay wants to make 24 but the recipe makes 8, then do the recipe 3 times to get 24 (8 x 3 = 24)

135 x 3 = 405

1 x 3 = 3

2 x 3 = 6

130 x 3 = 390

1 x 3 = 3

2 x 3 = 6

So Sanjay would need the following to make 24 pancakes:

405g flour

3tsp baking powder

6tbsps sugar

390mL milk

3 eggs

6tbsps oil

Answer:

405 g flour

3 tsb baking soda

6 tbsps sugar

390 mL milk

3 eggs

6 tablespoons oil

8
Which does NOT describe the quadrilateral below?
O A. trapezoid
B. square
C. parallelogram
О
D. rectangle

Answers

A: trapezoid. while trapezoids can have two right angles they are classified as having only one pair of parallel sides while the shape has two pairs

I need help surface area

Answers

Answer:

[tex]\huge\boxed{318yd^2}[/tex]

Step-by-step explanation:

The object shown in the diagram is a triangular prism, which contains two triangular sides and three rectangular sides.

The area of a triangle is simply [tex]\frac{bh}{2}[/tex].

Because the triangles are both the same, you may multiply the equation by 2 to get simply bh, or 9 * 6, or 54.  

Then, simply solve for the areas of each rectangle:

r1 = 11 * 7 = 77

r2 = 11 * 8 = 88

r3 = 11 * 9 = 99.

Then, simply add all the values to get:

99 + 88 + 77 + 54

318.

Hope it helps :) and let me know if you want me to elaborate.

helpppppppppppppppppppppppppppp

Answers

What do you need help with? Are you in danger?

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