Question

factor the polynomial.
$2x^2 + 13x - 7$
a $(x - 2)(x + 7)$
b $(x - 7)(2x + 1)$
c $(x + 7)(2x - 1)$
d $(2x + 7)(x - 1)$
e $(x - 7)(2x - 1)$

Explanation:

Step1: Expand Option A

Multiply \((x - 2)(x + 7)\): \(x^2 + 7x - 2x - 14 = x^2 + 5x - 14\), not \(2x^2 + 13x - 7\).

Step2: Expand Option B

Multiply \((x - 7)(2x + 1)\): \(2x^2 + x - 14x - 7 = 2x^2 - 13x - 7\), not \(2x^2 + 13x - 7\).

Step3: Expand Option C

Multiply \((x + 7)(2x - 1)\): \(2x^2 - x + 14x - 7 = 2x^2 + 13x - 7\), which matches the polynomial.

Step4: Expand Option D

Multiply \((2x + 7)(x - 1)\): \(2x^2 - 2x + 7x - 7 = 2x^2 + 5x - 7\), not \(2x^2 + 13x - 7\).

Step5: Expand Option E

Multiply \((x - 7)(2x - 1)\): \(2x^2 - x - 14x + 7 = 2x^2 - 15x + 7\), not \(2x^2 + 13x - 7\).

Answer:

C. \((x + 7)(2x - 1)\)