Synthetic Division and Remainder Theorem Quiz

If -1 is a root of f(x), which of the following must be true?

What dividend is represented by the synthetic division below?

Use synthetic division to solve (3x^4 + 6x^3 + 2x^2 + 9x + 10). What is the quotient?

What are all the roots of the function if one factor of f(x) = 5x^3 + 5x^2 - 170x + 280 is (x + 7)?

Use synthetic division to solve (x^3 + 1) ÷ (x - 1). What is the quotient?

What are all the roots of the function if one factor of f(x) = 4x^3 - 4x^2 - 16x + 16 is (x - 2)?

Use synthetic division to solve (2x^3 + 4x - 35x + 15) divided by (x - 3). What is the quotient?

Use synthetic division to solve (4x^3 - 3x^2 + 5x + 6) divided by (x + 6). What is the quotient?

What divisor is represented by the synthetic division below?

If f(1) = 0, what are all the roots of the function f(x) = x^3 + 3x^2 - x - 3?

If -1 is a root of f(x), then (x + 1) is a factor of f(x).
The dividend represented by synthetic division for the polynomial is 2x^3 + 10x^2 + x + 5.
Using synthetic division on (3x^4 + 6x^3 + 2x^2 + 9x + 10) results in a quotient of (3x^3 + 2x + 5).
For the polynomial (f(x) = 5x^3 + 5x^2 - 170x + 280) with a known factor (x + 7), the roots found using the Remainder Theorem are x = -7, x = 2, and x = 4.
Synthetic division of ((x^3 + 1)) by ((x - 1)) yields a quotient of (x^2 + x + 1 + \frac{2}{x - 1}).
For (f(x) = 4x^3 - 4x^2 - 16x + 16) with a factor (x - 2), the roots are x = -2, x = 1, and x = 2.
Dividing (2x^3 + 4x - 35x + 15) by ((x - 3)) through synthetic division produces a quotient of (3x^2 + 10x - 5).
The quotient obtained from synthetic division of (4x^3 - 3x^2 + 5x + 6) by ((x + 6)) is (4x^2 - 27x + 167 - \frac{996}{x + 6}).
The divisor shown in a synthetic division example corresponds to (x + 5).
Given that (f(1) = 0), the roots found for (f(x) = x^3 + 3x^2 - x - 3) are x = -3, x = -1, and x = 1.