Question

What is the correct factorization of x² + 13x + 30?

a. (x + 1)(x + 30)
b. (x + 2)(x + 15)
c. (x + 3) (x + 10)
d. (x + 5) (x + 6)

Answer 1

Answer: C. (x+3)(x+10)

Step-by-step explanation:

Note how the 3 and 10 are two values such that

• They add to 13, which is the middle coefficient, and,
• They multiply to 30, which is the last term

We can use the distribution rule like so to help confirm the answer

(x+3)(x+10)

y(x+10) ... replace x+3 with y

xy+10y .... distribute

x( y ) + 10( y )

x( x+3 ) + 10( x+3 ) .... plug in y = x+3

x^2+3x + 10x+30 .... distribute again twice more

x^2 + 13x + 30 ... combine like terms