How do you factor y=12r2+5r+3 ?

1 Answer
Jan 5, 2016

(3r+1)(4r+3) or indeed (3r+1)(34r)

Explanation:

to factor this trinomial 12r2+5r+3

compare to general form: ax2+bx+c

first multiply ac in this case 12×3=36

now consider the factors of - 36 which also add together to give b =5 in this question .

the pairs of factors of - 36 are ( - 2 , 18 ) reject as sum ≠ 5

( - 3 , 12 ) reject as sum ≠ 5

( - 4 , 9 ) accept as sum = 5

now rewrite the function as 12r24r+9r+3

(Note 5r has been replaced by 4r+9r)

factor the expression in pairs to give: 4r(3r+1)+3(3r+1)

(3r+1) is a common factor here

(3r+1)(4r+3)3

12r2+5r+3=(3r+1)(4r+3)