Question

How do you factor `15x^4-39x^3+18x^2`?

Answer 1

`=3x^2(x-2)(5x-3)`

Explanation:

Take out a common factor of `3x^2` first:

`15x^4 -39x^3 +18x^2`

`=3x^2(5x^2 -13x+6)`

Find factors of `5 and 6` whose products ADD to `13`

`" "5" and "6`
`" "darrcolor(white)(xxxx)darr`

`" "1 color(white)(xxxxx)2" "rarr 5 xx 2 = 10`
`" "5color(white)(xxxxx)3" "rarr 1xx3 = ul3`
`color(white)(xxxxxxxxxxxxxxxxxxx)13`

These are the correct factors: the signs in both brackets will be `-`

`=3x^2(5x^2 -13x+6)`

`=3x^2(x-2)(5x-3)`