Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M

Analyze the question: Both terms on the left have a common factor (x + 2). We factor it out and see what is left, which is M.

Concept: Common factor extraction: a·b + a·c = a(b + c).

Solution:

(x + 2)(x² − 3x + 2) + 2(x + 2)(x − 1)

Factor out (x + 2):

= (x + 2)[(x² − 3x + 2) + 2(x − 1)]

Expand inside the bracket:

= (x + 2)[x² − 3x + 2 + 2x − 2]

= (x + 2)[x² − x]

Comparing with (x + 2)M:

M = x² − x

Checking the options:

• A. (x + 2)²: no
• B. x(x + 2) = x² + 2x: no
• C. "xv + 2" looks like a typing error and is not equivalent to x² − x
• D. x² − x: matches

Tip: When you see the same bracket in every term, factor it out immediately. It saves you from expanding long cubic expressions. Also, x² − 3x + 2 = (x − 1)(x − 2), so the bracket could be written as (x − 1)[(x − 2) + 2] = (x − 1)x, which gives the same result.