Question

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) Theresa is correct because grouping should be done with ((3x²-18x)) and ((7x-42)).

b) Akash is correct because grouping should be done with ((3x²+7x)) and ((-18x-42)).

c) Both Theresa and Akash are correct, and either set of binomials can be used for grouping.

d) Neither Theresa nor Akash is correct, and a different grouping method should be used.

Answer 1

Theresa is correct because by grouping ((3x²-18x)) and ((7x-42)), we can factor out common factors from each binomial which leads to the factored form (3x+7)(x-6).

Step-by-step explanation:

The correct method for factoring the given polynomial expression (3x²+7x-18x-42) can be determined by examining the individual terms and seeing if there's a common factor in any grouping. Both Theresa and Akash propose different groupings but with the aim of factoring by grouping. Let's evaluate their suggestions.

Theresa suggests grouping the polynomial expression into ((3x²-18x)) and ((7x-42)), which allows us to factor out a common factor of 3x from the first binomial and 7 from the second binomial, resulting in (3x(x-6)+7(x-6)). Notice that (x-6) is a common binomial factor now, and the expression can be factored further into (3x+7)(x-6).

Akash's suggestion is to group the terms into ((3x²+7x)) and ((-18x-42)). Here, there are no common factors within the groupings, therefore this approach will not simplify the expression in a meaningful way. Therefore, the correct answer is:

a) Theresa is correct because grouping should be done with ((3x²-18x)) and ((7x-42)).