Question

FIND THE ERROR Given the polynomial expression 3x2+7x−18x−42, Theresa says you need to factor by grouping using the binomials (3x2−18x)and(7x−42). Akash says you need to use the binomials (3x2+7x) and (-18x-42). Is either of them correct? Justify your answer.

A. (3x² - 18x) and (7x - 42)
B. (3x² + 7x) and (-18x - 42)
C. (3x² + 7x) and (18x - 42)
D. (3x² - 18x) and (-7x - 42)

Answer 1

B, which groups the terms (3x² + 7x) and (-18x - 42) for factoring the polynomial 3x² + 7x − 18x − 42, leading to the factorization (x - 6)(3x + 7).

Step-by-step explanation:

The correct answer is option B: (3x² + 7x) and (-18x - 42). To factor the given polynomial expression 3x² + 7x − 18x − 42, we should group the terms in a way that allows us to factor by grouping. By choosing option B, we can factor out a common factor from each binomial. The first binomial, (3x² + 7x), has a common factor of x, and the second binomial, (-18x - 42), has a common factor of -6. Factoring these out, we get:

• x(3x + 7)
• -6(3x + 7)

Now we can see that both terms have a common binomial factor of (3x + 7), and so the expression can be factored further as:

(x - 6)(3x + 7)

This demonstrates that option B is the correct grouping that leads to successful factoring of the polynomial expression.