Question

Completely factor the given polynomial: 2x^2 - 8x - 10

Answer 1

Answer:
`2(x-1)(x+5)`

Explanation:

Factor
`2` out of
`2x^2`
`+~8x-10`

`Factor`
`2 ~out~ of ~2x^2`:

`2(x^2)+8x-10`

`Factor ~2~ out ~of ~8x`:

`2(x^2)+2(4x)-10`

`Factor ~2~ out~ of ~-10`:

`2x^2+2(4x)+2~x~-5`

`Factor ~2~ out~ of ~2x^2+2(4x):`

`2(x^2+4x)+2` ×
`-5`

`Factor ~2~out ~of ~2(x^2+4x)+2` ×
`-5:`

`2(x^2+4x-5)`

factor:

`Factor ~x^2+4x-5~ using ~the ~AC~ method.`

Consider the form
`x^2+bx+c.` Find a pair of integers whose product is
`c` and whose sum is
`b`. In this case, whose product is
`-5` and whose sum is
`4.`

`-1,5`

Write the factored form using these integers.

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

Remove unnecessary parentheses.

`=2(x-1)(x+5)` ← final answer

Answer 2

2(x - 5)(x + 1)

Explanation:

2x² - 8x - 10 ← factor out 2 from each term

= 2(x² - 4x - 5) ← factor the quadratic

consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)

the factors are - 5 and + 1 , since

- 5 × 1 = - 5 and - 5 + 1 = - 4 , then

x² - 4x - 5 = (x - 5)(x + 1)

then

2x² - 8x - 10 = 2(x - 5)(x + 1) ← in factored form