Fully factor the expressions below.

Question

a) x2 - 17x + 72
b) 10 x 2 + x - 3

Answer 1

a) x^2 - 17x + 72

The factors of 72 that add up to -17 (coefficient of x) are -8 and -9.

Therefore, we can rewrite the expression as:

x^2 - 8x - 9x + 72

Now, we can factor by grouping:

x(x - 8) - 9(x - 8)

Now, we can factor out the common binomial:

(x - 8)(x - 9)

The fully factored expression is (x - 8)(x - 9).

b) 10x^2 + x - 3

This expression cannot be factored further using simple integer factors. Therefore, the fully factored expression is 10x^2 + x - 3.