Quiz about Polynomial Functions Long Division and Synthetic Division Remainder Theorem

Question 1

Using the remainder theorem with the function below, which statements are false? Select all that apply.

$$f\left(x\right)=x^4+4x^3-x+3$$

Accepted Answer

The remainder when $$f\left(x\right)\div\left(x-1\right)$$ is -1.

Accepted Answer

The remainder when $$f\left(x\right)\div\left(x-3\right)$$ is -27.

Answer

The remainder when $$f\left(x\right)\div\left(x+3\right)$$ is -21.

Answer

The remainder when $$f\left(x\right)\div\left(x+1\right)$$ is 1.

Question 2

Given the quartic polynomial function $$f\left(x\right)=x^4+2x^3-8x^2-10x+15$$ with zeros $$x=1;\ x=-3$$ , use synthetic division to find the remaining zeros. Then, select the correct linear factorization from the options below.

Accepted Answer

$$\left(x-1\right)\left(x+3\right)\left(x+\sqrt[]{5}\right)\left(x-\sqrt[]{5}\right)$$

Answer

$$\left(x-1\right)\left(x+3\right)\left(x+\sqrt[]{5}i\right)\left(x-\sqrt[]{5}i\right)$$

Answer

$$\left(x+1\right)\left(x-3\right)\left(x+\sqrt[]{5}i\right)\left(x-\sqrt[]{5}i\right)$$

Answer

$$\left(x+1\right)\left(x-3\right)\left(x+\sqrt[]{5}\right)\left(x-\sqrt[]{5}\right)$$

Question 3

Question 3.

Accepted Answer

This is incorrect

Answer

This is correct

Question 4

If you use synthetic division to divide $$P\left(x\right)$$ by the root $$x=-2$$ and get a remainder of 0, then:

Accepted Answer

$$x+2$$ is a factor

Answer

$$x-2$$ is a factor

Question 5

Use synthetic division to determine the quotient and remainder when $$7x^3 - 14x^2 + 7x - 14$$ is divided by $$x - 2$$ .

Accepted Answer

Quotient: $$7x^2 - 14x + 7$$ , Remainder: $$0$$

Answer

Quotient: $$7x^2 - 14x + 28$$ , Remainder: $$42$$

Answer

Quotient: $$7x^2 + 14x - 28$$ , Remainder: $$-56$$

Answer

Quotient: $$7x^2 - 14x + 7$$ , Remainder: $$14$$

Question 6

Use synthetic division to divide $$2x^3 - 3x^2 + 4x - 5$$ by $$x - 2$$ .

Accepted Answer

$$2x^2 - x + 2$$

Answer

$$2x^2 + x - 2$$

Answer

$$2x^2 - 3x + 6$$

Answer

$$2x^2 + 3x - 6$$

Question 7

What is the remainder when x³ - 4 is divided by x + 2?

Accepted Answer

-12

Answer

0

Answer

-2

Answer

-6

Question 8

Decide if (x-3) is a factor of 3x³+10x²-x-12

Accepted Answer

No, it is not a factor!

Answer

Yes, it is a factor!

Question 9

Determine if (x+2) is a factor of 2x³-5x²+4x+8

Accepted Answer

Yes, it is a factor!

Answer

No, it is not a factor!

Question 10

Given the quartic polynomial function $$f\left(x\right)=x^4+2x^3-8x^2-10x+15$$ with zeros $$x=1;\ x=-3$$ , use synthetic division to find the remaining zeros. Then, select the correct linear factorization from the options given.

Accepted Answer

$$\left(x-1\right)\left(x+3\right)\left(x+\sqrt[]{5}\right)\left(x-\sqrt[]{5}\right)$$

Answer

$$\left(x-1\right)\left(x+3\right)\left(x+\sqrt[]{5}i\right)\left(x-\sqrt[]{5}i\right)$$

Answer

$$\left(x+1\right)\left(x-3\right)\left(x+\sqrt[]{5}\right)\left(x-\sqrt[]{5}\right)$$

Answer

$$\left(x+1\right)\left(x-3\right)\left(x+\sqrt[]{5}i\right)\left(x-\sqrt[]{5}i\right)$$

Question 11

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

Accepted Answer

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

Answer

Cam wrote the remainder incorrectly.

Answer

Cam added instead of subtracting the rows.

Answer

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

Question 12

Which would be better to use?

Accepted Answer

Long division

Answer

Synthetic division

Polynomial Functions Long Division and Synthetic Division Remainder Theorem

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