Factor the expression.

Question

Factor the expression. x2 + 17x + 72

A. (x + 1)(x + 72)

B. (x + 9)(x + 8)

C. (x - 9)(x - 8)

D. Prime Polynomial

Answer 1

x² + 17x + 72 = (x+a)(x+b)

 

We need two numbers, a and b, that multiply to give 72 and add to give 17.  The factors of 72 are:

 

72*1

36*2

18*6

12*6

9*8

 

Of these only 9 and 8 add to 17.  So the answer is (x+9)(x+8).

 

Check:

(x+9)(x+8) = x² + 8x + 9x + 72 = x² + 17x + 72   Check!