Factoring Polynomials and Trinomials

The video tutorial explains the process of factoring polynomials, emphasizing the importance of identifying the greatest common factor (GCF) before applying other techniques. It provides examples of factoring different types of polynomials, including those with a GCF, trinomials where the leading coefficient is not 1, and perfect square trinomials. The tutorial highlights common mistakes and demonstrates the correct approach to ensure complete factoring.

What is the first step in factoring any polynomial?

• Factor out the greatest common factor

• Factor as a difference of squares

• Factor as a perfect square

• Factor as a trinomial

Tags

CCSS.HSA.APR.C.4

In the expression 4x^2 - 64, what should be factored out first?

• 4

• 16

• 8

• x

Tags

CCSS.HSA.APR.C.4

Why is it incorrect to factor 4x^2 - 64 as a difference of squares initially?

• Because 64 is not a perfect square

• Because the GCF is not factored out

• Because x^2 is not a perfect square

• Because 4 is not a perfect square

When factoring a trinomial where the leading coefficient is not 1, what should you do first?

• Factor as a sum of cubes

• Factor as a difference of squares

• Factor as a perfect square

• Factor out the greatest common factor

In the trinomial x^2 + x - 12, what are the factors of -12 that add up to 1?

• 4 and -3

• 6 and -2

• 3 and -4

• 2 and -6

What is the GCF of the trinomial 3x^2 + 3x - 36?

• 12

• 1

• 3

• 9

Tags

CCSS.HSA.APR.C.4

What is the factored form of x^2 - 14x + 49?

• (x + 7)^2

• (x - 7)^2

• (x - 7)(x + 7)

• (x - 14)(x + 1)

What is the GCF of the trinomial 2x^2 - 28x + 98?

• 2

• 7

• 28

• 14

Tags

CCSS.HSA.APR.C.4

What is the factored form of 2(x^2 - 14x + 49)?

• 2(x - 14)(x + 1)

• 2(x + 7)^2

• 2(x - 7)^2

• 2(x - 7)(x + 7)

What should you always look for before trying any other factoring technique?

• The greatest common factor

• The sum of cubes

• The difference of squares

• The perfect square trinomial