Question

Factor f(x) = x2 + 10x + 16

Answer 1

To factor f(x) = x^2 + 10x + 16, we need to find two numbers whose sum is 10 and whose product is 16.

The two numbers are 2 and 8, since 2 + 8 = 10 and 2 × 8 = 16.

Therefore, we can write:

f(x) = x^2 + 10x + 16

= x^2 + 2x + 8x + 16

= (x^2 + 2x) + (8x + 16)

= x(x + 2) + 8(x + 2)

= (x + 2)(x + 8)

So the factorization of f(x) is (x + 2)(x + 8).