factor the basic trinomial:
2x^2 + 22x + 60
4x^3 - 4x^2 - 8x
For 2x^2 + 22x + 60:
First, find the factors of 2 * 60 that add up to 22:
2 * 60 = 120
Factors: 4 * 30, 6 * 20, 10 * 12
In this case, 10 and 12 add up to 22.
Rewrite the trinomial with these factors:
2x^2 + 10x + 12x + 60
Factor by grouping:
2x(x + 5) + 12(x + 5)
(x + 5)(2x + 12)
(x + 5)(2x + 12)
So, the factored form of 2x^2 + 22x + 60 is (x + 5)(2x + 12).
For 4x^3 - 4x^2 - 8x:
Factor out the common factor of 4x:
4x(x^2 - x - 2)
Factor the trinomial x^2 - x - 2:
x^2 - 2x + x - 2
x(x - 2) + 1(x - 2)
(x - 2)(x + 1)
Therefore, the factored form of 4x^3 - 4x^2 - 8x is 4x(x - 2)(x + 1).