Question 76029
trinomials  of the form {{{ax^2+bx+c}}} 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)