Question

How do you factor `50x^2-90x+16`?

Answer 1

`2(5x-1)(5x-8)`

Explanation:

Factor out the common constant `2`: `2(25x^2-45x+8)`

Find two `x`-terms that multiply to `25x^2`:

Possible choices:
`5x * 5x = 25x^2`
`25x * x = 25x^2`

Find two numbers that multiply to `8` and sum to `-45`. Since they must sum to a negative number, both numbers must be negative to multiply to `+8`.

Possible choices:
`-1 * -8 = 8`
`-2 * -4 = 8`

`2(25x^2-45x+8) = 2(5x -1) (5x -8)`

The `x`-term is found by multiplying the "insides" and "outsides" and summing: `-1*5x + 5x *-8 = -5x + (-40x) = -45x`

Therefore the solution is: `2(5x-1)(5x-8)`