Question

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

Answer 1

Yes

3x^2-30x-72

=3(x^2-10x-24)

=3(x^2-12x+2x-24)

=3{x(x-12)+2(x-12)}

3(x+2)(x-12)

Factors are

-2

and

12

Answer 2

Factors are: 3,(x−12),(x+2)

Explanation:

y=3x2−30x−72

By inspection, 3 is a factor →y=3(x2−10x−24)

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

These are 12 and 2.

Since the constant term is −ve the constants in the factors must have different sign. Also, since the coefficient of x is also −ve the larger factor of 24 must be −ve.

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

Therefore: y=3(x−12)(x+2)

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