Use the remainder theorem to determine if x = 4 is a zero of the following polynomial and find the quotient and the remainder
p(x) = x2 + 11x - 60
ОА.
Yes, x = 4 is a zero of the polynomial
The quotient is x + 15, and the remainder is 0.
ОВ.
No, x = 4 is not a zero of the polynomial
The quotient is x + 15, and the remainder is 0
OC Yes x = 4 is a zero of the polynomial.
The quotient is x + 7, and the remainder is 0
D
No, x = 4 is not a zero of the polynomial.
The quotient is x + 7, and the remainder is -88

Use The Remainder Theorem To Determine If X = 4 Is A Zero Of The Following Polynomial And Find The Quotient

Answers

Answer 1

Given:

The polynomial is

[tex]p(x)=x^2+11x-60[/tex]

To find:

Whether x = 4 is a zero of the given polynomial by remainder theorem and find the quotient and remainder.

Solution:

According to the remainder theorem, if (x-c) divides a polynomial p(x), then the remainder is p(c).

Divide the polynomial by (x-4) and check whether the remainder p(x)=0 at x=4.

Putting x=4 in the given polynomial, we get

[tex]p(4)=(4)^2+11(4)-60[/tex]

[tex]p(4)=16+44-60[/tex]

[tex]p(4)=60-60[/tex]

[tex]p(4)=0[/tex]

Since, remainder is 0, therefore, (x-4) is a factor of p(x) and x=4 is a zero.

Now, on dividing p(x) be (x-4) we get

[tex]\dfrac{x^2+11x-60}{x-4}=\dfrac{x^2+15x-4x-60}{x-4}[/tex]

[tex]\dfrac{x^2+11x-60}{x-4}=\dfrac{x(x+15)-4(x+15)}{x-4}[/tex]

[tex]\dfrac{x^2+11x-60}{x-4}=\dfrac{(x+15)(x-4)}{x-4}[/tex]

[tex]\dfrac{x^2+11x-60}{x-4}=x+15[/tex]

The quotient is x+15 and remainder is 0.

Therefore, the correct option is A.


Related Questions

i need help with pre-algebra, how do you convert exponential expressions? please help!

Answers

Answer:

Go on You Tube and look up

Converting Exponential Equations to Logarithmic Equations - College Algebra Tips

help 6th grade math i will give brainliest

Answers

Answer:

1. =     (all numbers powered by zeros are 1)

2. >    (the smaller the number gets when a number powers a fraction)

3. >    (-5)^2 will equal 25 but -5^2 will equal =25

Answer:

1. =

2. >

3. <

Step-by-step explanation:

2.5^0 = 1

1.5^0 = 1

(1/3)^4 = 0.0123

(1/3)^5 = 0.0041

5^1 = 5

-5^2 = 25

hope this helps. i am in algebra two so you can trust my answer. Happy Holidays! stay safe

7 less than 1/4 of x is y.
!!!ANSWER ASAP!!!

Answers

Answer: y= 1/4x -7

Step-by-step explanation:

f(n) = n^3– 2n
g(n)= 2n + 2
Find (f •g)(n)

Answers

Answer:

[tex]\boxed{(f~.~g)(x) = 2n^4 + 2n^3 - 4n^2 -4n}[/tex]

.

Step-by-step explanation:

We know that

[tex]f(n) = n^3 - 2n[/tex]

[tex]g(n) = 2n + 2[/tex]

.

So

[tex](f~.~g)(x) = f(n)~.~g(n)[/tex]

[tex](f~.~g)(x) = (n^3-2n)(2n + 2)[/tex]

[tex](f~.~g)(x) = n^3(2n + 2) - 2n(2n + 2)[/tex]

[tex](f~.~g)(x) = 2n^4 + 2n^3 - 4n^2 -4n[/tex]

Answer:

2jj2j wnqj qkwk abaia aow w wka a9w wjw a8uaaia sks sis s8siwobsisi shkahza a

Step-by-step explanation:

bs ak la ya s dyua youa au ab fusn aigska

Eric can read 3 pages in 7 minutes. Rob can read 8 pages in 14 minutes________. Response area is the faster reader because______ Response area

Answers

Answer:

Rob.

Step-by-step explanation:

If we take Eric's unit rate and multiply the denominator by two, it will be 14 minutes. Rob's denominator is also 14 minutes. This makes it easier on ourselves. If we multiply the bottom number we also have to multiply the top. So, on Eric's unit rate, we will take the 3 pages and mltiply it by 2 to get 6. 6 is less than 8, so Rob takes the win.

simplyfy: 4x + 8 + x -2 -3x​

Answers

4x+8+x-2-3x
5x +6-3x
2x+6 :D

Answer:

2x+6

Step-by-step explanation:

To simplify an expression such as this you must add like terms. Like terms are terms that have the same variable and power. In this expression 4x, x, -3x are like terms and -2 and 8 are also like terms. To add like terms simply add the coefficients and remember adding a negative is the same as subtracting. So, add the previously listed terms 4x + x + (-3x) = 2x, then -2+8= 6. This means the simplified expression is 2x+6.

Find zeros of the following equation
4x-3=x+2​

Answers

Answer:

4x-3=x+2

4x-x=3+2

3x=5

x=5/3

At a basketball camp there are 4 girls for every 5 boys. What is the ratio for BOYS to TOTAL number of campers?

Answers

Answer
5:9

hope this helps and have a wonderful day :)

There are nine campers in total. There are five boys in the camp. Here are the details:

Ratio: 5:9

Fraction: 5/9

Decimal: 0.5555...........

Percentage: 56%

Hope this helped! Have a wonderful Day! :D

witch expression is equivalent to |-5| + |3|
A -8
B -2
C 2
D 8​

Answers

Answer:

D

Step-by-step explanation:

WHEN APPLY MOD | | , we consider making every values in it positive.

so, equation becomes:

+5 + (+3)

= +8

therefore, D 8

Answer:

D

Step-by-step explanation:

The absolute value function always gives a positive result, that is

| - a | = | a | = a

Given

| - 5 | + | 3 |

= 5 + 3

= 8 → D

Simplify : - sqrt(- 75) A. - 5i * sqrt(2) B. - 5i * sqrt(3) C. - 5i D. 5i

Answers

Answer:

B

Step-by-step explanation:

Here, we want to calculate the square root of -√- (75)

That will be

-√(25)(-3)

= -5 √(-3)

√(-3) is same as 3i

So we have the root as;

-5i√3


Help need in 29 minutes

Answers

Answer:

d)

c)

Step-by-step explanation:

any more help just ask :)

More than 200 universities in the United States and many more worldwide have sport management programs. Approximately how many are accredited by the Commission on Sport Management Accreditation (COSMA)

Answers

Answer:

54 programs

Step-by-step explanation:

As of today's date 12/25/2020, there are a total of 54 programs that have been accredited by the Commission on Sport Management Accreditation (COSMA). Each university program that has been accredited can be found on COSMA's official website along with the date in which each program was officially accredited and the basic information regarding the program and its university. More and more programs are being added as time goes by.

help me with these questions

Answers

Answer:

for the graph all you do is graph the points

the slope is 2

y-intercept is 8

equation- y=2x+8

and 18 dollars for 5 pizzas

Step-by-step explanation:

5/6x for x =-8
Evaluate

Answers

the answer would be -20/3

Answer:

-20/3

Step-by-step explanation

5/6 x (-8)

-5/6  x 8    multiplying a( + )and a (-  )= a(-)  

-5/3  x 4     reduce with the greatest common factor 2

-20/3      

find the coordinates of the point which divides the line segment joining the points (4, -3) and (8.5) in the ratio 3:1 internally

Answers

Answer:

The coordinates of the division point are (7, 3)

Step-by-step explanation:

The coordinates of the point (x, y) which divides a segment with endpoints (x1, y1) and (x2, y2) at a ratio m1: m2 internally is ([tex]\frac{m1x2+m2x1}{m1+m2}[/tex] , [tex]\frac{m1y2+m2y1}{m1+m2}[/tex] ).

∵ The line segment joining the points (4, -3) and (8, 5)

x1 = 4 and x2 = 8

y1 = -3 and y2 = 5

∵ The point divides the segment at ratio 3: 1

m1 = 3 and m2 = 1

→ By using the rule above

∵ x = [tex]\frac{(3)(8)+(1)(4)}{3+1}[/tex] = [tex]\frac{24+4}{4}[/tex] = [tex]\frac{28}{4}[/tex]

x = 7

∵ y = [tex]\frac{(3)(5)+(1)(-3)}{3+1}[/tex] = [tex]\frac{15-3}{4}[/tex] = [tex]\frac{12}{4}[/tex]

y = 3

The coordinates of the division point are (7, 3)

Translate the inequality and solve. Three times a number is greater than six. 1 point​

Answers

Answer:

3x > 6

x > 2

Step-by-step explanation:

does that graph show a function explain how
A. No; the graph fills the vertical line test
B. Yes; the graph passes the vertical line test test
C. No; there are y-values that have more than one X-value
D. yes; there are no Y-values that have more than one X-value

Answers

I think it’s c because it look a

Express 25 as power with base 5​

Answers

Answer: express a number in base 5 notation you need to write it in powers of 5. ... 52 = 25 53 = 125 54 = 625. 625 is larger than 613 so I only need a 53 digit, a 52

Step-by-step explanation:

Answer:

POWERS OF 5:

.52 = 25

53 = 125

54 = 625

So 625 is larger than 613

so you will only need 53

but then you also will have 52 so you have 52 as your answer i hope this helps :)

Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!

Answers

Answer:

3

Step-by-step explanation:

9 / 54 = x / 18

x = 3

what is the percent change of 44000 to 40000

Answers

Answer:

10 percent

Step-by-step explanation:

40000 is the old value and 44000 is the new value. In this case we have a positive change (increase) of 10 percent because the new value is greater than the old value.

Three items were bought at a car boot sale.
Item A
Mass = 42 grams
Volume = 2 cm
Item B
Mass = 87.5 grams
Volume 5 cm3
Item C
Mass = 147 grams
Volume = 7 cm3
=

The density of platinum is approximately 21 grams per cmº.
Which of the items cannot be platinum?
You must show your working.

Answers

Answer: Multiply the density with the volume. You get 2418.2 grams or 2.4182 kilograms

Step-by-step explanation:

Answer:

Item B

Step-by-step explanation:

A:

density = mas/volume = 42 g / 2 cm^3 = 21 g/cm^3    

This may be platinum.

B.

density = mass/volume = 87.5 g / 5 cm^3 = 17.5 g/cm^3

This cannot be pure platinum.

C.

density = mass/volume = 147 g / 7 cm^3 = 21 g/cm^3

This may be platinum.

Answer: Item B

A store is having a sale with 10% off everything.

b) Does your equation for part a represent a proportional relationship?

Answers

Answer:

what equation can you give more through instructions please

Select all of the following that are quadratic equations.


1. x2 + 3 x -5 = 0
2. x2 - x = 3 x + 7
3. 5 x - 7 = 0
4. 7 x2 + 14 x = 0
5. x3 - 3 x2 + 1 = 0
6. x - 5 = 9 x + 7

Answers

Answer:

1. x² + 3x - 5 = 0

2. x² - x = 3 x + 7

4. 7x² + 14x = 0

Step-by-step explanation:

A Quadratic equation takes the form;

ax² + bx + c = 0

a, b, c are constants and a cannot be 0.

Options 1 fits this;

x² + 3x - 5 = 0

Option 2 fits this as well;

x² - x = 3 x + 7  

x² -x - 3x - 7 = 0

x² - 4x - 7 = 0

Option 4 fits this as well if c = 0.

7x² + 14x + 0 = 0

I’m very confused on this! Where do I even start on here?? This is extra credit for my geometry class !

Answers

U can start from
Any where let’s say just pick one triangle and just solve them and just put the answer it even shows where for example like b=

Encuentra la ecuacion de la parabola con vertice en el origen y foco en las cordenadas 0,1en su forma ordinaria y general

Answers

Answer:

[tex]x^{2}=4y[/tex]

[tex]y=\frac{1}{4}x^{2}[/tex]

Step-by-step explanation:

Forma ordinaria

La ecuación de la parabola de manera ordinaria está dada por:

[tex](x-h)^{2}=4p(y-k)[/tex] (1)  

Donde:

(h,k) es la coordenda del vértice, en nuestro caso (0,0) ya que está en el origen.(h,k+p) es la coordenda del foco, en nuestro caso (0,1).

Por lo tanto h = 0, k = 0 y p = 1.

Remplazando estos valores en la ecuación de la parábola, tenemos:

[tex](x-0)^{2}=4*1(y-0)[/tex]

[tex]x^{2}=4y[/tex] (2)

 

Forma general  

La forma general de una parábola esta dada por la siquiente ecuación

[tex]y=ax^{2}+bx+c[/tex]

Reordenando la ecuación (2) tenemos:

[tex]y=\frac{1}{4}x^{2}[/tex]

Espero esto te haya ayudado!

Which expression represents a positive number? A. -9.8 x (-23.5) B. 9.8 x (-23.5) C. 23.5 x (-9.8) D. -23.5 x 9.8

Answers

Answer: Option A

Step-by-step explanation: if we multiply two negative numbers we get a positive result, pls give brainliest

Answer:

A represents a positive number

Step-by-step explanation:

(−9.8) x (-23.5) = 230.3x

If a polynomial 2x( raised to power 3) -9x +15x +p, when divided by (x-2), leaves -p as remainder, then p is equal

Answers

Answer:

p is -5

Step-by-step explanation:

If a polynomial 2x³-9x² +15x +p is divided by (x-2), then the remainder is gotten by equating the divisor x - 2 to zero

If x - 2 = 0

Add 2 to both sides

x - 2 + 2 = 0 + 2

x = 2

Substitute x = 2 into the expression to get the remainder:

If p(x) = 2x³-9x² +15x +p

p(2)= 2(2)³-9(2)² +15(2) +p

p(2) = 2(8) - 9(4) + 30 + p

p(2) = 16-36+30+p

p(2) = -20 + 30 + p

p(2) = 10+p

Since the remainder given in question is - p, to get p, we will equate p(2) to -p as shown

p(2) = -p

10+p = -p

10 = -p-p

10 = -2p

p = 10/-2

p = -5

Hence the value of p is -5

pls help meh with this <3​

Answers

Answer:

For the first one, 29,000 s, 29,500 s, and 29,999 s.

For the second one, no because the bookcase is taller than the doorway.

Oof hope I'm correct and was able to help <3

Does anybody know the average individual score for a Mathcounts competition?

Answers

Answer:

4.0 hope this helps!!6

On the first day, 8 adult tickets were sold and 13 student tickets were sold for a total of $75. On day two, 10 adult tickets were sold and 9 student tickets were sold for a total of $72. What is the cost of an adult ticket? What is the cost of a student ticket?

Answers

Answer:

Adult ticket = $4,5

Student ticket = $3

.

Step-by-step explanation:

Let say adult ticket is x and student ticket is y. so we get:

→ 8x + 13y = 75 (×5) 40x + 65y = 375

→ 10x + 9y = 72 (×4) 40x + 36y = 288

.

Eliminate both equations

40x + 65y = 375

40x + 36y = 288    

29y = 87

[tex]y = \frac{87}{29}[/tex]

[tex]y = 3[/tex]

.

Substitute the value of y to one of equations

[tex]10x + 9(3) = 72[/tex]

[tex]10x + 27 = 72[/tex]

[tex]10x = 72 - 27[/tex]

[tex]10x = 45[/tex]

[tex]x = \frac{45}{10}[/tex]

[tex]x = 4,5[/tex]

.

Happy to help :)

Answer:

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Step-by-step explanation:

wjis sisi sjaijs aibaia aihwoh ha ajj w

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