Question

Which of the following statements best describes the "grouping method" of factoring trinomials?

Answer 1

Answer:

• B. The grouping method of factoring trinomials involves rewriting the bx term into the factors that fit the particular trinomial, and factoring these four terms using grouping

Explanation:

The description may be better explained by applying it to an example.

Example:

• trinomial: x² - x - 30

• the general form of a trinomial is a x² - bx - 30

• comparing with x² - x - 30 the bx term is - x

• then you must rewrite the bx term, - x, into two terms whose coefficients are factors of 30:

          Two numbers which add up - 1 and multipled are - 30. Those numbers are - 6 and + 5, because -6 + 5 = - 1 and (-6) × (+5) = -30.

           Hence, the two terms are -6x and 5x, and the expression rewritten is:

            x² - 6x + 5x - 30

• factor these four terms using grouping:

            (x² - 6x) + (5x - 30)

            x(x - 6) + 5(x - 6)

            (x - 6) (x + 5)

Hence, the factored trinomial is (x - 6) (x + 5)