Factoring Polynomials: Double Grouping Quiz
Which shows one way to determine the factors of 12x3 - 2x2 + 18x - 3 by grouping? 2x2(6x - 1) + 3(6x - 1) 2x2(6x - 1) - 3(6x - 1) 6x(2x2 - 3) - 1(2x2 - 3) 6x(2x2 + 3) + 1(2x2 + 3)
A.) 2x2(6x - 1) + 3(6x - 1)
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 2x + 7 −2x2 + 7 2x2 + 7
B.) 2x + 7
Which polynomial is prime? 3x3 + 3x2 - 2x - 2 3x3 - 2x2 + 3x - 4 4x3 + 2x2 + 6x + 3 4x3 + 4x2 - 3x - 3
B.) 3x3 - 2x2 + 3x - 4
Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? x(x2 + 4) + 5(x2 + 4) x2(x + 4) + 5(x + 4) x2(x + 5) + 4(x + 5) x(x2 + 5) + 4x(x2 + 5)
B.) x2(x + 4) + 5(x + 4)
Factor x3 - 4x2 + 7x - 28 by grouping. What is the resulting expression? (x2 - 4)(x + 7) (x2 + 4)(x - 7) (x2 - 7)(x + 4) (x2 + 7)(x - 4)
D.) (x2 + 7)(x - 4)
Which polynomial is prime? x3 + 3x2 - 2x - 6 x3 - 2x2 + 3x - 6 4x4 + 4x3 - 2x - 2 2x4 + x3 - x + 2
D.) 2x4 + x3 - x + 2
Which shows one way to determine the factors of x3 + 5x2 - 6x - 30 by grouping? x(x2 - 5) + 6(x2 - 5) x(x2 + 5) - 6(x2 + 5) x2(x - 5) + 6(x - 5) x2(x + 5) - 6(x + 5)
D.) x2(x + 5) - 6(x + 5)
Which shows one way to determine the factors of x3 - 12x2 - 2x + 24 by grouping? x(x2 - 12) + 2(x2 - 12) x(x2 - 12) - 2(x2 - 12) x2(x - 12) + 2(x - 12) x2(x - 12) - 2(x - 12)
D.) x2(x - 12) - 2(x - 12)
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. Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) - (8x2 + 4). In Step 2, Faelyn should factor only 2x out of the first expression. Faelyn should factor out a negative from one of the groups so the binomials will be the same.
NOT B.) Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) - (8x2 + 4).
Factor -8x3 - 2x2 - 12x - 3 by grouping. What is the resulting expression? (2x2 - 3)(4x + 1) (-2x2 - 3)(-4x + 1) (2x2 - 3)(-4x + 1) (-2x2 - 3)(4x + 1)
NOT C.) (2x2 - 3)(-4x + 1)
