Question

Factor the polynomial 8x2 - 50

Answer 1

2(2x - 5)(2x + 5)

Explanation:

`8x^(2) -50`

First pull out 2.

2
`(4x^(2) -25)`

We can see each is a square after pulling out 2.

square root of 4 is 2 and square root of 25 is 5. Because the we have - 25 we know we have opposite signs, two - would make a positive, and two + would also make a positive, and the middle wouldn't cancel out. So we have:

2(2x - 5)(2x +5)

Let's check our work. Focus on the ( ) first.

2(2x - 5)(2x + 5)

2x * 2x + 2x * 5 - 5 * 2x - 5 * 5

4
`x^(2)` + 10x - 10x - 25

4
`x^(2)` - 25 Can't forget to multiply by 2!

2 (4
`x^(2)` - 25 )

8
`x^(2)` - 50