2.4 Dividing Polynomials; Remainder and Factor Theorems

​2.4 Dividing Polynomials; Remainder and Factor Theorems

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

Multiple Choice

This work shows $$x^2-3x+5\div x-2$$  . What information does this reveal? #2

• x-2 is not a factor of $$x^2-3x+5$$   since the remainder is 3.

• x-2 is a factor of $$x^2-3x+5$$   since the remainder is 3.

Match

Match the following: #5

• is a factor of $$5x^2-10x-40$$  

• is a solution of $$5x^2-10x-40$$  

• 0

• x+2

x + 2...

-2...

The remainder is...

5x² -10x - 40 is being divided by...

• x + 2...

• -2...

• The remainder is...

• 5x² -10x - 40 is being divided by...

Multiple Choice

Complete the problem shown here.

Use the remainder to determine whether 5 is a solution of $$p\left(x\right)=2x^3-12x^2+11x-5$$  .#8

• 5 is a solution of p(x) since the remainder is 0.

• 5 is a solution of p(x) since the remainder is 100.

• 5 is not a solution of p(x) since the remainder is 0.

• 5 is not a solution of p(x) since the remainder is 100.

Multiple Choice

The work here shows that dividing $$x^2+16$$  by x+4 results in a remainder of 32. Which statement is true based on the work shown here? #10

• -4 is a solution of $$x^2+16$$  

• 4 is a solution of $$x^2+16$$

• x+4 is not a factor of $$x^2+16$$  

• x-4 is not a factor of $$x^2+16$$  

Multiple Choice

Complete the synthetic division and use the remainder to determine a true statement concerning p(x) and its solutions. #11

• -2 is a solution of p(x) since the remainder is equal to 0.

• -2 is not a solution of p(x) since the remainder is equal to 1.

• -2 is not a solution of p(x) since the remainder is equal to 33.

• 2 is not a solution of p(x) since the remainder is equal to -1.

Multiple Choice

Assume that a polynomial has a solution at the x-value 4.

Which of the following must be a factor of that same polynomial? #15

• 4x

• x-4

• x+4

Multiple Choice

What is the remainder when  a³ - 4 is divided by a+2? #19

• -2
• -6
• -12
• 0

Multiple Choice

Finish dividing $$p\left(x\right)=5x^3+34x^2+26x+C$$   by x+6. Determine what value C must equal if x+6 is a factor of p(x). #17

• C would need to be equal to 0.

• C would need to be equal to 12.

• C would need to be equal to -12.

• C would need to be equal to 300.

Multiple Choice

Which binomial is a factor of f(x)= x³ -6x² +3x +10? #18

• x + 1
• x + 2
• x + 5
• x + 10

Multiple Choice

Which binomial is a factor of  f(x)= x³ + x² -24x +36? #20

• x + 2
• x + 3
• x + 6
• x + 9

Multiple Choice

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)? #21

• -25
• 25
• 113
• -113

Multiple Choice

What is the proper way to write the answer for the following problem? #26

• 2x³-x²-25x-12
• 2x⁴-x³-25x²-12x+0

Multiple Choice

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake? #28

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.

Multiple Choice

It's time to write the answer. What goes in the yellow area? #30

• $$n-9$$

• 9

• -9

• $$6n^2-48n-58$$

Multiple Choice

What is the next step in the synthetic division? #32

• Add the -48 to the 54

• Multiply the 54 and 6

• Divide the 54 by 6

• Bring down the -58

Multiple Choice

$$\left(4x^4-8x^3-3x^2+7x-2\right)\div\left(2x-1\right)$$  

Use long division to evaluate. #36

• $$2x^3-3x^2-3x+2$$  

• $$2x^3+3x^2+3x+2$$  

• $$2x^3-3x^2-3x-2$$  

• $$2x^3+2$$  

Multiple Choice

Solve using long division. $$\left(8x^2+6x-20\right)\div\left(4x-5\right)$$  . #38

• $$2x-4$$  

• $$2x+4$$  

• $$2x-1-\frac{16}{4x-5}$$  

• $$2x-4-\frac{40}{4x-5}$$

Multiple Choice

Is this division problem worked correctly? #39

• This is correct!
• This is incorrect!