Question

4z-3 is a factor of 4z2-13z-12​

Answer 1

Answer:

(z - 4) • (4z + 3)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(22z2 - 13z) - 12

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 4z2-13z-12

The first term is, 4z2 its coefficient is 4 .

The middle term is, -13z its coefficient is -13 .

The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 4 • -12 = -48

Step-2 : Find two factors of -48 whose sum equals the coefficient of the middle term, which is -13 .

-48 + 1 = -47

-24 + 2 = -22

-16 + 3 = -13 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 3

4z2 - 16z + 3z - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

4z • (z-4)

Add up the last 2 terms, pulling out common factors :

3 • (z-4)

Step-5 : Add up the four terms of step 4 :

(4z+3) • (z-4)

Which is the desired factorization

Final result:

(z - 4) • (4z + 3)