SOLUTION: Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime. Help. 9p^2+6p-8 6q^2-13q+6 Cannot you show work please

Algebra ->  Equations -> SOLUTION: Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime. Help. 9p^2+6p-8 6q^2-13q+6 Cannot you show work please      Log On


   

Question 76029: Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime.
Help.
9p^2+6p-8
6q^2-13q+6 Cannot you show work please
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
trinomials of the form ax%5E2%2Bbx%2Bc may be factored into (dx+e)(fx+g) where e and g are factors of c, and d and f are factors of a

remember that positive numbers may have negative factors...keep an eye on the correct sign requirements

b is the sum of the products of the factors of a and c

taking the factors of the product of a and c will show the products that sum to b

for the first equation...the product of a and c is -72...the factors of -72 that sum to b are 12 and -6

the factors of a are (9 and 1) and (3 and 3)...the factors of c are (+-1 and +-8) and (+-2 and +-4)

9 is not an integer factor of 12 or -6 so the a factors are (3 and 3)...to get 12 and -6, the c factors must be (4 and -2)

so the factors of the equation are (3p+4)(3p-2)

for the second equation...a X c is 36... factors that sum to b are -4 and -9

factors of a are (1 and 6) and (2 and 3)...factors of c are (1 and 6) and (2 and 3)
since both products are negative, one pair of factors will be negative

6 is not an integer factor of -4 or -9 so the a factors are (2 and 3)...the c factors must be (-2 and -3)

so the factors of the second equation are (3q-2)(2q-3)