Factor x^3+2x^2-36x-72
x^3+2x^2-36x-72
use "grouping"
x^2(x+2) - 36(x+2)
= (x+2)(x^2 - 36)
= (x+2)(x+6)(x-6)
To factor the given expression x^3 + 2x^2 - 36x - 72, we can use the method of factoring by grouping.
Step 1: Group the terms in pairs:
(x^3 + 2x^2) + (- 36x - 72)
Step 2: Factor out the common terms from each group:
x^2(x + 2) - 36(x + 2)
Step 3: Notice that both terms in the parentheses are the same. Factor out the common factor of (x + 2):
(x + 2)(x^2 - 36)
Step 4: Further factor the quadratic expression (x^2 - 36) by recognizing it as a difference of squares:
(x + 2)(x - 6)(x + 6)
Therefore, the factored form of the expression x^3 + 2x^2 - 36x - 72 is (x + 2)(x - 6)(x + 6).