Question

1. Factor completely: 2a^2 + 6a + 18

2. Factor completely: 5x^2 − 5
3. Factor completely: 3t^3 + 18t^2 − 48t
4. Factor completely: 4n − n^3

Answer 1

`2(a+3)(a+3)`

`5(x+1)(x-1)`

`3t(t-2)(t+8)`

`n(2+n)(2-n)`

Explanation:

Factor each expression

`2a^2 + 6a + 18`

`2(a^2 + 3a + 9)`

product =9 and sum =6

3 times 3 is 9

3 plus 3 is 6

`2(a+3)(a+3)`

2. Factor completely: 5x^2 − 5

GCF is 5

`5x^2 - 5`

`5(x^2 - 1)`

`5(x+1)(x-1)`

3. Factor completely: 3t^3 + 18t^2 − 48t

`3t^3 + 18t^2 -48t`

`3t(t^2 + 6t -16)`

product is -16 and sum is 6

-2 times 8 = -16

-2+8=6

`3t(t^2 + 6t -16)`

`3t(t-2)(t+8)`

4. Factor completely: 4n − n^3

`n(4 -n^2)`

`n(2+n)(2-n)`