Question 1

Use synthetic division to divide the polynomial $$-7x^4$$ + $$2x^3$$ - $$5x^2 + 9x + 1$ by x + 1$. What is the quotient?

Accepted Answer

$$-7x^3$$ - $$5x^2 + 0x + 9$

Question 2

Which of the following is the correct setup for synthetic division when dividing $$-7x^4$$ + $$2x^3$$ - $$5x^2 + 9x + 1$ by x + 1$?

Accepted Answer

Use $$-1 as $$the synthetic divisor and the coefficients $$-7, 2, -5, 9, 1$$

Question 3

After performing synthetic division on $$-7x^4$$ + $$2x^3$$ - $$5x^2 + 9x + 1$ by x + 1$, what is the remainder?

Accepted Answer

$$-8$$

Question 4

Which of the following best describes the relationship between the divisor $$x + 1$$ and the synthetic divisor used in the process?

Accepted Answer

The synthetic divisor is the opposite sign of the constant in $$x + 1$$

Question 5

If the remainder from synthetic division is not zero, what does this indicate about $$x + 1 as a $$factor of $$-7x^4$$ + $$2x^3$$ - $$5x^2 + 9x + 1$?

Accepted Answer

$$x + 1 is $$not a factor of the polynomial

Question 6

Which of the following is the correct sequence of coefficients to use for synthetic division of $$-7x^4$$ + $$2x^3$$ - $$5x^2 + 9x + 1$?

Accepted Answer

$$-7, 2, -5, 9, 1$$

Question 7

What is the degree of the quotient when dividing a degree 4 polynomial by a linear divisor?

Accepted Answer

Degree 3

Question 8

Which of the following best describes the purpose of synthetic division?

Accepted Answer

To quickly divide a polynomial by a linear factor of the form $$x - c$$

Question 9

If you perform synthetic division and the remainder is $$0$$, what does this tell you about the divisor?

Accepted Answer

The divisor is a factor of the polynomial

Question 10

Which of the following is NOT a valid use of synthetic division?

Accepted Answer

Dividing by $$x^2 + 1$

Polynomial Division: Synthetic Division in College Algebra

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