Factoring trinomials with a non-1 leading coefficient by grouping

u12_l2_t1_we3 Factoring trinomials with a non-1 leading coefficient by grouping

we cannot factor out a 4 since 15 is not divisible by 4.

we must factor by grouping. look for 2 numbers whose product equals the product of 4 and -15

their sum needs to be equal to positive 4

the first clue is the product of the numbers is negative, so a and b must have different signs

but a + b is equal to 4

so, the difference of their absolute values must equal 4

let's think about all of the factors of -60

6 band 10 look tantalizing since they are 4 apart

we want them to add to positive 4, so larger number must be positive

so, we want positive 10 and negative 6

now, group first 2 terms

now, group the second 2 terms. both are divisible by 5

factor out a 2y

now, factor out a 5