Question

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

Choose the correct answer below.
O A. The grouping method of factoring trinomials involves separating the first and last terms of the trinomial into respective factors, and then factoring by
grouping
OB. 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
OC. The grouping method of factoring trinomials involves factoring out the common factor.

Answer 1

The grouping method of factoring trinomials involves separating the first and last terms of the trinomial into respective factors, and then factoring by grouping.

Step-by-step explanation:

The correct answer is A. The grouping method of factoring trinomials involves separating the first and last terms of the trinomial into respective factors, and then factoring by grouping. In this method, we find two pairs of terms with common factors and group them together. Then, we factor out the greatest common factor from each pair. Finally, we factor out a common factor from the resulting binomials. Let's consider an example:

Example:

Factor the trinomial: x^2 + 5x + 6

Step 1: Separate the first and last terms: x^2 + 5x + 6 = (x^2 + 2x) + (3x + 6)

Step 2: Factor out the greatest common factor from each pair: x(x + 2) + 3(x + 2)

Step 3: Factor out a common factor from the resulting binomials: (x + 2)(x + 3)

Therefore, the factored form of the trinomial x^2 + 5x + 6 is (x + 2)(x + 3).

Answer 2

• 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

Step-by-step 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)