Fully factor the expressions below.
a) x2 - 17x + 72
b) 10 x 2 + x - 3
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.