Can y= 3x^2-30x-72 y=3x2−30x−72 be factored? If so what are the factors ?

1 Answer
Alan N.
Apr 29, 2016

Yes.
Factors are: 3, (x-12), (x+2)3,(x−12),(x+2)

Explanation:

y = 3x^2-30x-72y=3x2−30x−72
By inspection, 3 is a factor -> y=3(x^2-10x-24)→y=3(x2−10x−24)

Since the constant term is -24−24 and the coefficient of xx is -10−10, we now look for factors of 2424 which differ by 1010

These are 12 and 2.

Since the constant term is -ve−ve the constants in the factors must have different sign. Also, since the coefficient of xx is also -ve−ve the larger factor of 2424 must be -ve−ve.

Hence the second and third factors are (x-12) and (x+2)(x−12)and(x+2)

Therefore: y =3(x-12)(x+2)y=3(x−12)(x+2)

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