Question

How do you factor `6p^2 - p - 15`?

Answer 1

`(2p+3)(3p-5)`

Explanation:

`6p^2-p-15`
if it helps, think about it like this: `ap^2-bp-c`

First, multiply "a" and "c"
`6*-15=-90`

Find 2 factors of -90 that give you -1 (or the b-value) when you add them

1,-90 doesn't work because it adds to -89
2, -45 doesn't work because it adds to -43
3, -30 doesn't work because it adds to -27
5, -18 doesn't work because it adds to -13
6, -15 doesn't work because it adds to -9
9,-10 Works because it adds to `-1` !!

Now that you got the two factors of -90 that add up to -1, set it all up in this format: `(p+9/a)(p-10/a)`

so you'll get:
`(p+9/6)(p-10/6)`

simplify
`(p+3/2)(p-5/3)`

if you can't simplify anymore, take the denominator and make it p's coefficient and now you are finished
`(2p+3)(3p-5)`

If you're still stuck, use these helpful links:

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khan academy