How do you factor the trinomial #15r^2+2rs-s^2#?

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Answer 1 · 2017-05-02T15:01:59

(3r+1)(5r-1)

This is a simple application of factoring.

15 can be factored into 3 and 5 (the combination of 1 and 15 is very unlikely), and we see that 5-3=2, so that is good.

The equation has a #r^2# and a #s^2# in there, so the equation can be factored into (ar+bs) (cr+ds)

We already know what a and c might be, so let's plug them in: (3r+bs) (5r+ds)

In order to get 2rs, we have +5-3. So b=1, d=-1

And we get #-s^2#, which is perfect.

So the answer is: (3r+1)(5r-1)