Factoring Polynomials Completely Assignment

Consider the polynomial 6x2 - 8x + 2. What is the GCF of the polynomial? What is the equivalent factored form of the polynomial?

2 2(3x - 1)(x - 1)

Which polynomials are prime? Check all that apply. 2x2+ 7x + 1 5x2 - 10x + 5 3x2 + 8 4x2 - 25 x2 + 36

A C E

Which are the prime factors of the polynomial 24x4 - 3x? Check all that apply. 2x 3x (4x2 + 1) (2x - 1) (x - 1) (4x2 + 2x + 1) (2x2 - 2x + 1)

B D F

Which diagram shows the X method being used correctly to factor the trinomial 2x2 - 3x + 1?

C

Which product of prime polynomials is equivalent to 30x3 - 5x2 - 60x? 5(2x2 - 3)(3x + 4) x(10x + 3)(3x - 4) 5x(2x - 3)(3x + 4) 5x(2x + 3)(3x - 4)

C

Completely factor the polynomial 8x2 - 24x + 20x - 60. 8x(x + 3)(x - 5) (4x - 3)(2x - 5) 2(2x - 3)(2x + 5) 4(x - 3)(2x + 5)

D

Factor the polynomial completely. 4x3 - 12x2 + 7x - 21 4x2(x - 3) + 7(x - 3) Which is the completely factored polynomial? 4x2(x + 4) 3x2(x - 3) (4x2 - 7)(x + 3) (4x2 + 7)(x - 3)

D

On a test, Leo is asked to completely factor the polynomial 3x3 - 3x + 5x2 - 5. He uses double grouping to get (x2 - 1)(3x + 5). Has he factored the polynomial completely? Explain.

No, Leo's answer is not a product of prime polynomials because x2 - 1 can be factored. This is a difference of squares. He should continue factoring to get (x - 1)(x + 1)(3x + 5).

Describe the first step when factoring any polynomial. Why is this the first step? Explain.

The first step when factoring any polynomial is to factor out the GCF. The GCF is the greatest common factor for all the terms of the polynomial. By factoring out the GCF first, the coefficients and constant term of the polynomial will be reduced.

Determine the GCF for each of the polynomials. 2x3 - 7x2 + 3x The GCF is ___. 33x4 - 22 The GCF is ___. 24x5 - 56x3 + 16x The GCF is ___.

x 11 8x