The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, squared, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=
Answers
Answer:
(x-2)(x+3)(x+6)
Step-by-step explanation:
Given the polynomial function p(x)=x^3+7x^2-36
We are to write it as a product of its linear factor
Assuming the value of x that will make the polynomial p(x) to be zero
Let x = 2
P(2) = 2³+7(2)²-36
P(2) = 8+7(4)-36
P(2) = 8+28-36
P(2) = 0
Since p(2) = 0 hence x-2 is one of the linear factors
Also assume x = -3
P(-3) = (-3)³+7(-3)²-36
P(-3) = -27+7(9)-36
P(-3) = -27+63-36
P(-3) = 36-36
P(-3) = 0
Since p(-3) = 0, hence x+3 is also a factor
The two linear pair are (x-2)(x+3)
(x-2)(x+3) = x²+3x-2x-6
(x-2)(x+3) = x²+x-6
To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.
x^3+7x^2-36/x²+x-6 = x+6
Hence the third linear factor is x+6
x^3+7x^2-36 = (x-2)(x+3)(x+6)
Answer:
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Step-by-step explanation:
Here we want to rewrite the polynomial
P(x) = x^3 + 7x^2 - 36
As a product of linear factors given that we have one of the roots already as (x + 3)
What we shall do here is to divide the polynomial by x + 3
Please check attachment for long polynomial division
From the division, the other factor is x^2 + 4x -12
So we can rewrite the polynomial as;
x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)
So let’s now write x^2 + 4x -12 as a product of its linear factors
x^2 + 4x -12 = x^2 + 6x -2x -12
= x(x + 6)-2(x + 6)
so we have;
(x -2)(x + 6)
Therefore;
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Related Questions
Vinnie is 1/2 as old as Julie Julie is 24 how old is vinnie
Answers
Answer:
Vinnie is 12.
Step-by-step explanation:
24 divided by 2 is 12
A fraction is the representation of a decimal number so the fraction of 1/2 of 24 is 12 thus its age of Vinnie is 12 years.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers, but the division is not wholly complete.
For example, 1/3 is a fraction and in decimal, it is 0.333. Here 1 will be called a numerator while 3 will be the denominator.
Given that,
Age of Julie = 24 years
Age of Vinnie = 1/2 of 24
The 1/2 fraction of 24 will be
⇒ 24/2 = 12 years.
Hence "The fraction of 1/2 of 24 is 12 thus the age of Vinnie is 12 years".
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3. 100x2-36y2 ??
ito pa guys pleasedddd!!
Answers
Answer:
4(5x - 3y)(5x + 3y)
Step-by-step explanation:
Assuming you require the expression factored.
Given
100x² - 36y² ← factor out 4 from each term
= 4(25x² - 9y²) ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
25x² - 9y²
= (5x)² - (3y)² ← with a = 5x and b = 3y
= (5x - 3y)(5x + 3y)
Thus
100x² - 36y² = 4(5x - 3y)(5x + 3y) ← in factored form
21st term: 3, 8, 13, 18 ?
Answers
Answer: 108
Step-by-step explanation:
I can’t answer this question
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
The radicals get in the way a bit, so we can define ...
x = √p
y = √q
Then the equation is ...
(x +y)/(1-x) = (4x+y)/(1-x^2)
Multiplying by (1-x^2), we have ...
(x +y)(1 +x) = 4x +y . . . . . . using 1-x^2 = (1-x)(1+x) the 1-x factor cancels
x^2 +xy +x +y = 4x +y . . . eliminate parentheses
x(x +y) = 3x . . . . . . . subtract (x+y)
x +y = 3 . . . . . . . . . . divide by x
This is the sum we're looking for:
√p +√q = 3
Answer: The answer is 3
Step-by-step explanation:
What is the value of x?
(5х)
110°
110°
70
14
Answers
Answer:
The answer to your question is :The value of 5× = 110°
PLEASE HELP ASAP!! I'LL GIVE YOU BRAINLIEST!!
Answers
Answer:
-5
Step-by-step explanation:
This is the correct answer, I messed up at first so I edited it. (my bad)
HURRY UP NEED HELP
7. Find the equation of a line that fits the data shown in the graph below.
Answers
Answer:
y=-x+3/2, I hope that I hoped, and by the way, it is NEGATIVE x. It's a little hard to see :P
Answer:
y=2x + (-1)
Slope is m=2 and the y-intercept is b= -1
- 1 1/4 divided by 36
Answers
-2.75 divided by 36 = -0.07638 with the line on top because the 8 repeats
Find the quotient 122 and -2.
A. 124
B. 61
C. 61
D. 120
Answers
Answer:
C
Step-by-step explanation:
The true answer is -61
Tip: If you want the correct answer you can not have a typo. Just a heads up.
Drag the cards to create a number that matches these rules.
The number ends in the tenths place.
8 is the nearest one when rounding
Answers
Brad sells each cup of lemonade for $0.50 he wrote.
Answers
Answer:
What are we supposed to solve??? its incomplete
Step-by-step explanation:
Find the 18th term of this arithmetic sequence:
12, 26, 40, 54,...
Answers
Answer:
djzkbhjejbebdhhfhhffhfhfhhfhfffhhfhfjfjfjf#/!cupcupcupcupFairmont
ASAP want your guys opinion about this
What do you think of when you hear the word "Math"?
Answers
Answer:
I think of hard work :)
Step-by-step explanation:
Answer:
The perfect answer would be
M-ental
A-buse
T-o
H-uman
Step-by-step explanation:
hehe, pls mark me brainliest if you can:)
If BC measures 8 inches, the approximate area of circle B is
square inches.
Answers
The area of the circle radius as 8 inches will be 201.062 inches².
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Given the circle with a radius BC of 8 inches.
Area of circle = πr² where r is the radius of the circle.
So,
Area = π(8)² = 201.062 inches.
Hence "The area of the circle radius as 8 inches will be 201.062 inches².
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The given question figure is missing the figure has been attached below;
2/15 of an airline's flights are international. The airline's flights are equally divided among 8 countries. What fraction of the airline's flights are to each country? If the airline has 2700 flights in all, how many are international? How many are not international? How many are to each of the 6 countries?
Answers
Answer:
The fraction of the airline's flights for each country is 1 /60
The number of international airline flights is 360 flights
The number of flights for each of the 8 countries is 45 flights
Step-by-step explanation:
Given;
international airline's flights = 2/15
number of countries = 8
total number of the airline flight
The fraction of the airline's flights for each country;
[tex]= \frac{2}{15}*\frac{1}{8} \\\\ = \frac{1}{60}[/tex]
The number of international airline flights;
[tex]= \frac{2}{15} *2700\\\\= 360 \ flights \ are \ international[/tex]
The number of flights for each of the 8 countries;
[tex]= \frac{1}{8} *360\\\\= 45 \ flights \ \\\\OR\\\\= \frac{1}{60}*2700\\\\ = 45 \ flights[/tex]
1. David uses 1 tbsp of sugar for every 1.25 cups of water when he makes lemonade complete the table below by filling in the missing values
Answers
Answer:
Step-by-step explanation:
David uses 1 table spoon of sugar for every 1.25 cups of water to prepare lemonade.
Therefore, Number of table spoons of sugar required (S) ∝ Cups of water required (w)
⇒ S ∝ w
⇒ S = kw
⇒ k = [tex]\frac{S}{w}[/tex]
⇒ k = [tex]\frac{1}{1.25}[/tex] = 0.8
So the formula to calculate the amount of water will be,
S = 0.8w
⇒ w = [tex]\frac{S}{0.8}[/tex]
where k = proportionality constant
Now we can complete the table with the help of the formula.
Sugar (tbsp) Water (cups)
1 1.25
7 8.75
3 3.75
5 6.25
What is an equation of the line that passes through the points
(0,8) and
(−8,−4)? Put your answer in fully reduced form.
Answers
y+4 = 1.5 (x+ 8)
y+4 = 1.5x + 12
1.5x - y = -12+4
1.5x - y = -8
Answer:
Answer given in the photo
Marsha gave the cashier 20 to pay for 3 pairs or socks.
Answers
First, you must subtract.
$20 - $5.03 = $14.97This is because he recieved $5.03 in exchange.
Next, you must divide by 3.
$14.97 / 3 = $4.99
Therefore each pair of socks costs $4.99.
Hope this helps!
A truck used 6.3 gallons of gasoline to travel 105 miles. How many gallons of gasoline would it need to travel 250 miles? A 15 gallons B 4,166.7 gallons С 150 gallons D 16.7 gallons
Answers
Answer:
a
Step-by-step explanation:
got it right in my test
graph y = -3/2x - 3 .
Answers
Answer:
hope this helps
Step-by-step explanation:
Answer:
you have to graph it urself, but what you have to do is but the starting point at -3, and go down 3 on the y-axis, and up 2 on the x-axis. you can also go up 3 on the x-axis, and 2 down on the y-axis. i hope this explained it and helped you :)
Step-by-step explanation:
What is the solution to 3x-10x+5=5x+17
Answers
Answer:
x = -1
Step-by-step explanation:
3x - 10x + 5 = 5x + 17 (collect like terms)
-7x + 5 = 5x + 17 (subtract 5x on both sides)
-12x + 5 = 17 ( subtract 5 on each side)
-12x = 12 ( divide by -12 on each side)
x = -1
Answer:
x = - 1
Step-by-step explanation:
[tex]3x - 10x + 5 = 5x + 17[/tex]
Add the like terms.
[tex] - 7x + 5 = 5x + 17[/tex]
Add 7x to both sides.
[tex]5 = 12x + 17[/tex]
Subtract 17 from both sides.
[tex] - 12 = 12x[/tex]
[tex] - \frac{12}{12} = x[/tex]
[tex] - 1 = x[/tex]
If you can answer this question please do it as soon as you can.
Answers
(3^8 x 2^ -5 x 9^0)^ -2 x (2^-2/3^3)^4 x 3^28
Any non-zero expression raised to the power of equals
Step 2:(3^8 x 2^-5 x 1)^-2 x (2^-2/ 3^3)^4 x 3^28
Step 3: (3^8 x 2^-5 x1)^-2 x 2^-8/ 3^12 x 3^28
Any expression multiplied by remains the same
Step 4 : (3^8 x 2^-5)^-2 x 2^-8/3^12 x 3^28
To raise a product to a power, raise each factor to that power
Step 5 : 3^-16 x 2^10 x 2^-8/ 3^12 x 3^28
Reduce the expression with
Step 6: 3^-16 x 2^10 x 2^-8 x 3^16
Calculate the product
2^2
Evaluate , and then your answer is 4!!!!
Tisha paid $10.50 for 6 liters of her favorite soda. To the nearest cent, how much did 3 liters of her
favorite soda cost?
Answers
Answer:
$5.25
Step-by-step explanation:
Step 1:
10.50 / 6 = x / 3 Equation
Step 2:
6x = 31.5 Multiply
Step 3:
x = 31.5 ÷ 6 Divide
Answer:
x = 5.25
Hope This Helps :)
A clothing business finds there is a linear relationship between the number of shirts n it can sell and the price P it can charge per shirt. In particular historical data shows that 2 thousand shirts can be sold at a price of 80 dollars each, and that 5 thousand shirts can be sold at a price of 65 each
Answers
Answer:
We have two data points:
2000 shirts can be sold for $80 each.
5,000 shirts can be sold for $65 each.
Then we can define the relation:
P(n).
Where P is the price, and n is the number of shirts.
Now, we know that we can model this as a linear relationship that passes through the points (2000, $80) and (5000, $65)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, the slope is:
a = ($65 - $80)/(5000 - 2000) = -$0.005.
Then our equation is:
P(n) = -$0.005*n + b
Now let's find the value of b, we know that:
P(2000) = $80 = -$0.005*2000 + b
$80 = -$10 + b
$80 + $10 = b = $90
Our equation is:
P(n) = -$0.005*n + $90.
please help. i will mark brainleast
Answers
Answer:
9 is the answer.
Both negative signs cancel eachother, so you just have 45/5.
Step-by-step explanation:
Good luck! <3
Diana is buying plates and cups for a party. She wants the same number of each. Plates are sold in packs of eight and cups are sold in packs of 12. What is the least number of plates and cups she can buy? How many packs of plates? How many packs of cups? Explain how you know.
Answers
Answer:
The least number of plates and cups she can buy is 24
She will buy 3 packs of plates
She will buy 2 packs of cup
Step-by-step explanation:
Plates = 8 per pack
Cups = 12 per pack
Find the Lowest common multiple of 8 and 12
8 = 16, 24, 32, 40, 48, 56, 64, 72, 80
12 = 24, 36, 48, 60, 72
What is the least number of plates and cups she can buy?
The Lowest common multiple of 8 and 12 is 24
The least number of plates and cups she can buy is 24
How many packs of plates?
Packs of plates = 24 plates / 8 per pack
= 3 packs
She will buy 3 packs of plates
How many packs of cups?
Packs of cups = 24 / 12 per pack
= 2 packs
She will buy 2 packs of cup
I already know that the answer is 190 but why
Answers
Answer:
You know that the total number of persons is 20 , so every person shakes hands with 19 persons.. It then mean that, there are 20×19=380 handshakes. But by every handshake two persons are involved. Therefore, 380 is the result of double-counting, which gives 190 handshakes.Step-by-step explanation:
Hope this helpsExpress x in terms of y:
3(x + 2y) = 2x = 5y
Answers
Answer:
-6y=x
Step-by-step explanation:
3x+6y=2x=5y
Subtract 5y from all
3x+y=2x-5y
subtract y and 2x from both sides
x=-6y
Help, please. I will give brainliest to anyone that answers first.
Answers
Answer:
5000 I think bc 5 times 1000 is 500
Answer:
Step-by-step explanation:
1000 meter = 1 kilometer
1 km= 1000 meter
constant proportionality
y/x=k
y is km , x is meter
1/1000=k
y=1/1000 x (x is the number of meters)
meter Km
250 0.25
12 12/1000=0.012
1 1/1000
kilometer meter
5 5000
20 20000
0.3 300
What is the remainder when 69,694 is divided by 93?
Answers
Answer:
37
hope this helps :3
37 is the remainder when 69,694 is divided by 93
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find the remainder when 69,694 is divided by 93
The number which is getting divided here is called the dividend.
69694 is dividend
The number which divides a given number is the divisor.
93 is the divisor.
the number which we get as a result is known as the quotient.
The divisor which does not divide a number completely produces a number, which is referred to as remainder.
69694 can be written as (69657+37)
69657 is divisible completely by 93 and the remainder is 37.
Hence, 37 is the remainder when 69,694 is divided by 93
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