Quiz about Remainder Theorem and Factor Theorem

Question 1

According to this work, is x-3 a factor of $$p\left(x\right)=5x^3-2x^2+x-120$$ ?

Accepted Answer

Yes, x-3 is a factor of p(x) since the remainder is 0.

Answer

No, x-3 is not a factor of p(x) since the remainder is 0.

Question 2

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

Accepted Answer

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

Answer

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

Question 3

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

Accepted Answer

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

Answer

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

Question 4

What do we know about p(x)= $$3x^4+2x^3-5x+4$$ based off of the work shown here?

Read carefully. Only one statement is true.

Accepted Answer

1 is not a solution of p(x)

Answer

1 is a solution of p(x)

Answer

x -1 is a factor of p(x)

Answer

x+1 is not a factor of p(x)

Question 5

This work shows $$x^3+2x^2-58x-35\div x-7$$ . What does this reveal?

More than one answer is correct.

Accepted Answer

x-7 is a factor of p(x).

Accepted Answer

7 is a solution of p(x).

Answer

x+7 is a factor of p(x).

Answer

-7 is a solution of p(x).

Question 6

Which statement accurately describes what this work demonstrates?

Accepted Answer

x+6 is not a factor of $$x^3-x^2-40x\ +13$$ .

Answer

x+6 is a factor of $$x^3-x^2-40x\ +13$$ .

Answer

x-6 is not a factor of $$x^3-x^2-40x\ +13$$ .

Answer

x-6 is a factor of $$x^3-x^2-40x\ +13$$ .

Question 7

Complete the problem shown here.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

Complete the problem shown here.

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

Accepted Answer

x-5 is a factor of p(x) since 5 was a solution.

Answer

x-5 is not a factor of p(x) since 5 was not a solution.

Answer

x+5 is not a factor of p(x) since 5 was not a solution.

Answer

x+5 is a factor of p(x) since 5 was a solution.

Question 9

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

Accepted Answer

x+4 is not a factor of $$x^2+16$$

Answer

-4 is a solution of $$x^2+16$$

Answer

4 is a solution of $$x^2+16$$

Answer

x-4 is not a factor of $$x^2+16$$

Question 10

This work shows $$4x^2+17\div x+2$$ .

Accepted Answer

True

Answer

False

Question 11

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 12

Complete the rest of this synthetic division problem.

Determine the remainder.

Accepted Answer

The remainder is 18.

Answer

The remainder is 0.

Answer

The remainder is 108.

Answer

The remainder is 28.

Question 13

Based on the remainder you found, which statement is true?

Accepted Answer

3 is not a solution of $$2x^3-15x+9$$ .

Answer

3 is a solution of $$2x^3-15x+9$$ .

Answer

-3 is a solution of $$2x^3-15x+9$$ .

Answer

-3 is not a solution of $$2x^3-15x+9$$ .

Question 14

Based on the remainder you found, which statement is true?

Accepted Answer

x-3 is not a factor of $$2x^3-15x+9$$ .

Answer

x-3 is a factor of $$2x^3-15x+9$$ .

Answer

x+3 is not a factor of $$2x^3-15x+9$$ .

Answer

x+3 is a factor of $$2x^3-15x+9$$ .

Question 15

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

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

Accepted Answer

x-4

Answer

4x

Answer

x+4

Question 16

Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?

Accepted Answer

The x-value 2

Answer

The x-value -2

Answer

The x-value 0

Question 17

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).

Accepted Answer

C would need to be equal to 12.

Answer

C would need to be equal to 0.

Answer

C would need to be equal to -12.

Answer

C would need to be equal to 300.

Remainder Theorem and Factor Theorem

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