How do you factor $15x^2 – 25x – 60$ ?

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Answer 1 · 2016-04-05T16:17:53

$15x^2-25x-60=5(3x+4)(x-3)$

To factorize a polynomial of general form $ax^2+bx+c$ , one should divide middle term $bx$ in two parts, whose sum is $b$ and product is $axxc$ .

So for $15x^2-25x-60$ , we should divide $-25x$ in two parts which add up to $-25$ and whose product is $15xx(-60)=-900$ .

A few trial indicate them to be $-45$ and $20$ . Hence

$15x^2-25x-60=15x^2-45x+20x-60$ or

$15x(x-3)+20(x-3)$ or

$(15x+20)(x-3)$ or $5(3x+4)(x-3)$

How do you factor 15x^2 – 25x – 6015x^2 – 25x – 60?