Factoring and Finding Zeros with Synthetic Division

What does the Factor Theorem state?

• If the polynomial is zero, the remainder is a factor of the divisor.

• If the divisor is zero, the remainder is a factor of the polynomial.

• If the remainder is non-zero, the divisor is a factor of the polynomial.

• If the remainder is zero, the divisor is a factor of the polynomial.

In the example F(x) = 3x^3 - 4x^2 - 28x - 16, what is the first step in synthetic division when given that x + 2 is a factor?

• Multiply the coefficients by 2.

• Divide the coefficients by -2.

• Bring down the coefficients and use 2 in synthetic division.

• Bring down the coefficients and use -2 in synthetic division.

After performing synthetic division on F(x) = 3x^3 - 4x^2 - 28x - 16 with x + 2, what is the resulting polynomial?

• 3x^2 - 10x - 8

• 3x^2 - 4x - 16

• 3x^2 + 10x + 8

• 3x^2 + 4x + 16

What is the fully factored form of F(x) = 3x^3 - 4x^2 - 28x - 16?

• (x + 2)(3x - 2)(x + 4)

• (x + 2)(3x + 2)(x - 4)

• (x - 2)(3x + 2)(x + 4)

• (x - 2)(3x - 2)(x - 4)

In the example F(x) = x^3 - 6x^2 + 5x + 12, what is the factor given?

• x - 4

• x + 4

• x - 3

• x + 3

What is the final factored form of F(x) = x^3 - 6x^2 + 5x + 12?

• (x + 4)(x + 3)(x - 1)

• (x - 4)(x + 3)(x - 1)

• (x + 4)(x - 3)(x + 1)

• (x - 4)(x - 3)(x + 1)

When finding the zeros of F(x) = x^3 - 2x^2 - 23x + 60, what is one of the zeros given?

• x = 2

• x = -3

• x = 3

• x = -2

What are the zeros of F(x) = x^3 - 2x^2 - 23x + 60?

• 5, -3, -4

• -5, 3, 4

• 5, 3, -4

• -5, -3, 4

Given that F(-2) = 0, what is one of the zeros of the polynomial?

• 3

• 2

• -2

• -3

What are the zeros of the polynomial that factors to (x + 7)(x - 1)?

• 7, 1

• 7, -1

• -7, 1

• -7, -1