Question

factor completely: $2x^2 + x - 10$

a $(x + 5)(x - 4)$

b $(2x + 5)(x + 2)$

c $(2x + 5)(x - 2)$

d $(2x - 2)(x + 5)$

Explanation:

Step1: Expand Option A

\((x + 5)(x - 4)=x^2 - 4x + 5x - 20=x^2 + x - 20\) (not equal to \(2x^2 + x - 10\))

Step2: Expand Option B

\((2x + 5)(x + 2)=2x^2 + 4x + 5x + 10=2x^2 + 9x + 10\) (not equal to \(2x^2 + x - 10\))

Step3: Expand Option C

\((2x + 5)(x - 2)=2x^2 - 4x + 5x - 10=2x^2 + x - 10\) (matches the given quadratic)

Step4: Expand Option D

\((2x - 2)(x + 5)=2x^2 + 10x - 2x - 10=2x^2 + 8x - 10\) (not equal to \(2x^2 + x - 10\))

Answer:

C. \((2x + 5)(x - 2)\)