Advanced Math practice question

Answer: A. (2x + 1)(x + 3)

The leading coefficient 2 must come from 2x · x, and the constant 3 from the two constants. Try (2x + 1)(x + 3): the outer and inner products are 6x + x = 7x. Check: 2x² + 6x + x + 3 = 2x² + 7x + 3.

Why the other answers are wrong

B. (2x + 3)(x + 1)

(2x + 3)(x + 1) gives a middle term of 2x + 3x = 5x, not 7x. The 1 and 3 are in the wrong factors.

C. (2x − 1)(x − 3)

(2x − 1)(x − 3) has the right size of middle term but the wrong sign: −6x − x = −7x.

D. (x + 1)(x + 3)

(x + 1)(x + 3) is x² + 4x + 3 — the leading coefficient 2 is missing.

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