Factoring Polynomials: Double Grouping Quiz

Factor 6x4 - 5x2 + 12x2 - 10 by grouping. What is the resulting expression?

(6x2 - 5)(x2 + 2)

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?

(x2 + 1)(x + 1)

Factor x3 - 4x2 + 7x - 28 by grouping. What is the resulting expression?

(x2 + 7)(x - 4)

The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.10x3 + 35x2 − 4x − 14 5x2(____) − 2(____)What is the common factor that is missing from both sets of parentheses?

2x + 7

Which shows one way to determine the factors of 12x3 - 2x2 + 18x - 3 by grouping?

2x2(6x - 1) + 3(6x - 1)

Which polynomial is prime?

2x4 + x3 - x + 2

Which polynomial is prime?

3x3 - 2x2 + 3x - 4

Which polynomial is prime?

9x3 + 11x2 + 3x - 33

Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 - 8x2 + 3x2 + 4. Her work is shown. Step 1: (6x4 - 8x2) + (3x2 + 4) Step 2: 2x2(3x2 - 4) + 1(3x2 + 4) Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?

Faelyn should realize that her work shows that the polynomial is prime.

Which shows one way to determine the factors of x3 + 11x2 - 3x - 33 by grouping?

x2(x + 11) - 3(x + 11)

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?

x2(x + 4) + 5(x + 4)

Which shows one way to determine the factors of x3 + 5x2 - 6x - 30 by grouping?

x2(x + 5) - 6(x + 5)

Which shows one way to determine the factors of x3 - 12x2 - 2x + 24 by grouping?

x2(x - 12) - 2(x - 12)