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

Step-by-step

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.

8

step-by-step explanation:

this is a subtraction problem.

10 - 2 = 8

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct