Factor each polynomial if possible. If the polynomial cannot be factored using integers, write 'prime,'

1) 12q^2+34q-28

2) 18h^2+15h-18

3) 12p^2-22p-20

4) 8z^2+20z-48

First one,

12q^2+34q-28

divide whole thing by 2

6q^2+17q-14

use trial and error and get (2x+7) (3x-2)

factored out form is (2) (2x+7) (3x-2)

2.

divide by 3

6h^2+5h-6

trial and error and get (2x+3) (3x-2)

so the factored form is (3) (2x+2) (3x-2)

3. divide by 2

6p^2-11x-10

use trial and error and get (2x-5) (3x+2)

the factored out form is (2) (2x-5) (3x+2)

4. divide by 4

2z^2+5z-12

use trial and error and get (x+4) (2x-3)

the factored form is (4) (x+4) (2x-3)

to factor the basic thing is

ax^2+bx+c

b=x+y

ac=xy

solve for x and y

so exg 2z^2+5z-12

a=2

b=5

c=-12

2 times - 12=-24

then factctor - 24 and find factors that add up to 5

-1, 24

-2, 12

-3, 8

-4,6

now add

-1+24=23

-2+12=10

-3+8=5 check

-4+6=2

the numbers are - 3 and 8

split it into such

2z^2+8z-3z-12

group (2z^2+8z) + (-3z-12)

undistribute using distributive property

ab+ac=a (b+c)

(2z) (z+4) + (-3) (z+4)

now reverse distribute again

((2z) + (-3)) (z+4)

(2z-3) (z+4)