quadratic expression factoring

Question

factor the expression.

 

 x2 + 13x + 40

A. (x + 1)(x + 40)

B.  (x + 8)(x + 5)

C. (x - 8)(x - 5)

D. Prime Polynomial

 

Answer 1

A = 1, B = 13, C = 40.

 

Is it possible for a pair of factors of C (40) that sum up to B (13)?

 

Factor pairs of 40: ±1 & ±40, ±2 & ±20, ±4 & ±10, ±5 & ±8.

 

5 + 8 = 13 and (5)(8) = 40.

 

So, x² +13x + 40 =

 

x² + (5x + 8x) + 40 =

 

x(x + 5) + 8(x+5) =

 

(x + 8)(x + 5).