Factor this trinomial completely. - 12x^2+45x+12

Step-by-step Answer:

Step 1:

Extract factor (s) common to all terms.

In this case, the HCF is 3, so the expression is written

-12x^2+45x+12 = - 3 (4x^2-15x-4)

The negative sign was also exrracted to give a positive leading coefficient, which is easier to work with.

Step 2, group the coefficient in such a way that there is a common factor.

Leaving the factor - 4 for the moment, and concentrate on the coefficients in parentheses, write the original expression as

4x^2 - 15x - 4

= 4x^2 - 16x

+ x - 4

= 4x * (x-4) + 1 * (x-4)

extract (x-4) as a common factor

= (x-4) (4x+1)

Step 3:

Combine all the factors to get

-3 (x-4) (4x+1)

=3 (4-x) (4x+1)

as the complete factoring of the given expression.

Answer: - 12x^2 + 45x + 12

-3 (4x^2 - 15x - 4)

-3 (4x + 1) (x - 4)

Step-by-step explanation:

D.