Question

(08.03 MC)

Factor completely 2x2 + 2x − 24. (5 points)

2(x − 3)(x + 4)
(2x − 3)(x + 8)
2(x − 4)(x + 6)
(2x − 6)(x + 4

Answer 1

2(x − 3)(x + 4)

Explanation:

We have to factor the expression
`2x^2+2x-24`

Factor out GCF which is 2

`2(x^2+x-12)`

We can write the middle term as : x = 4x-3x

`2(x^2+4x-3x-12)`

Now, we factor out GCF as follows

`2(x(x+4)-3(x+4))`

Now, factored out the common term

`2((x+4)(x-3))`

First option is correct.

Factored form is given by 2(x − 3)(x + 4)

Answer 2

2(x + 4)(x - 3)

The trick here is to notice that all 3 terms can be div. by 2:

2(x^2 + x - 12)

Note that -12 factors into -3 * 4 or -4 * 3. The pair {4, -3} leads to the correct sign for the middle term of the product.

x^2 + x - 12 = (x + 4)(x - 3), and so 2x2 + 2x − 24 = 2(x + 4)(x - 3).