Question

(07.03 MC)

Factor completely 2x2 − 16x + 30.

2(x + 3)(x + 5)
2(x − 3)(x + 5)
2(x − 5)(x + 3)
2(x − 5)(x − 3)

Answer 1

2(x - 5)(x - 3)

Explanation:

2x² - 16x + 30 ← factor out 2 from each term

= 2(x² - 8x + 15) ← factor the quadratic

consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (- 8)

the factors are - 5 and - 3 , since

- 5 × - 3 = + 15 and - 5 - 3 = - 8 , then

x² - 8x + 15 = (x - 5)(x - 3)

then

2x² - 16x + 30 = 2(x - 5)(x - 3)