Polynomial Skills Quiz

Identify the factors of the polynomial: 2x^2 + 5x - 3

• (2x + 1)(x - 3)

• (2x + 3)(x - 1)

• (2x - 3)(x + 1)

• (2x - 1)(x + 3)

Using the remainder theorem, find the remainder when f(x) = 3x^3 - 2x^2 + 5x - 7 is divided by x - 2

• The remainder is 11

• The remainder is 0

• The remainder is -3

• The remainder is 5

Apply the factor theorem to determine if x - 3 is a factor of the polynomial: 4x^3 - 9x^2 + 6x - 9

• Yes, x - 3 is not a factor of the polynomial.

• Yes, x - 3 is a factor of a different polynomial.

• Yes, x - 3 is a factor of the polynomial.

• No, x - 3 is not a factor of the polynomial.

Perform polynomial division: (3x^3 + 2x^2 - 5x + 7) ÷ (x - 1)

• Quotient: 2x^2 + 3x + 7, Remainder: 5

• Quotient: 3x^2 - 5x + 7, Remainder: 2

• Quotient: 3x^2 + 5x + 0, Remainder: 7

• Quotient: 4x^2 + 2x + 7, Remainder: 3

Calculate the remainder using the remainder theorem for f(x) = 2x^3 - 4x^2 + 3x - 5 divided by x + 1

• -2

• 1

• -5

• 3

Check if x + 2 is a factor of the polynomial: 2x^3 + 3x^2 - 5x + 6 using the factor theorem

• No, x + 2 is not a factor of the polynomial 2x^3 + 3x^2 - 5x + 6.

• No, x - 2 is a factor of the polynomial.

• Yes, x + 2 is a factor of the polynomial.

• Yes, x - 2 is not a factor of the polynomial.

Divide the polynomials: (4x^3 - 3x^2 + 2x - 1) ÷ (x + 2)

• 4x^2 - 11x + 24 - 49/(x + 3)

• 4x^2 - 11x + 24 - 49/(x - 2)

• 4x^2 - 11x + 24 - 49/(x + 2)

• 4x^2 - 11x + 24 + 49/(x + 2)

Identify the factors of the polynomial: 3x^3 - 6x^2 + 3x

• 3x(x-1)^2

• 3x^2(x-1)

• 3x(x-1)

• 3(x-1)^2

Find the remainder when f(x) = x^3 - 2x^2 + 3x - 4 is divided by x - 3 using the remainder theorem

• -5

• 2x - 1

• 7

• 14

Determine if x - 1 is a factor of the polynomial: 2x^4 - 3x^3 + 5x^2 - 4x + 2 by applying the factor theorem

• Yes, x - 1 is a factor of the polynomial.

• No, x - 1 is a factor of the polynomial.

• No, x - 1 is not a factor of the polynomial.

• x - 1 is not a factor of the polynomial.