Factoring out the GCF from a polynomial then factoring further

The video tutorial explains how to factor a polynomial expression by first identifying and extracting the greatest common factor (GCF). It then demonstrates how to factor the remaining trinomial by identifying two numbers that multiply to the last term and add to the middle term. The process is shown step-by-step, emphasizing the importance of writing the expression as a product of its factors.

What is the first step in factoring the polynomial 3M^3 + 12M^2 + 9M?

• Subtract the smallest term

• Multiply all terms

• Add all coefficients

• Find the greatest common factor

After factoring out the GCF from 3M^3 + 12M^2 + 9M, what expression is left?

• M^2 + 3M + 4

• 3M^2 + 4M + 3

• 3M^2 + 3M + 4

• M^2 + 4M + 3

What is the purpose of rewriting a polynomial as a product of its factors?

• To change the variable

• To simplify the expression

• To add more terms

• To increase the degree of the polynomial

Which two numbers multiply to 3 and add to 4 in the trinomial M^2 + 4M + 3?

• 3 and 1

• 1 and 3

• 4 and 0

• 2 and 2

What are the factors of the trinomial M^2 + 4M + 3?

• (M + 4)(M + 0)

• (M + 1)(M + 1)

• (M + 2)(M + 2)

• (M + 3)(M + 1)