Factoring Trinomials: Not-So-Easy Version

Factoring Trinomials Part 2. Learn how to factor trinomials with a leading coefficient in less time than it takes to Spiderman to suit up.

to factor trinomials of the form ax

squared plus bx

plus c we have to work a little harder

but we're going to start the same way by

noticing that there's no gcf

so we have to split it into two sets of

parentheses and we need to start out by

figuring what two terms are going to

multiply to get 6x squared

this could be 3 times 2 or it could be 6

times 1.

we don't really know then we have to

look at the 5 in the back and say well

what two numbers multiply to get 5.

now we have to run through our possible

pairings of beginning pairs and ending

pairs what if we start with six

x and one x and we put a five and a one

what if we start with six x and one x

and we switch it make it a one and a

five or potentially what if we start with three

x and two x and have one and 5

or if we start with 3x and 2x and switch

it and make it 5 and 1.

these are all our possibilities here how

do we know which one will work we need

the pair that can help us get our middle

term of 13x

the first pair will give us a 5 and a 6.

this doesn't add up to 13.

the second pair will give us a 1 and a

30 again not going to work for us but

the third pair gives us a 2 and a 15.

that can combine to get 13 and the last

pair won't work either so we know the

pairing that will work for us will be 3x

and 2x

and 1 and 5. then we put in our signs to

make sure when we multiply this out we

end up with a 13x in the middle

you can always double check by

completing the foil method to see that

indeed we have it correct and the signs

are right

3x minus 1 times 2x plus 5 is our answer