Question

How do I solve: 4y^2 - 11y - 3 =0 by factoring?

Answer 1

Well, do you know how to factor by decomposition?

Answer 2

by decomposition?

Answer 3

Yeah, we compose the middle term into smaller terms

Answer 4

decompose*

Answer 5

yes I do

Answer 6

but if I do that: (2y-...)(2y-...)

Answer 7

So what two numbers sum up to -11, and are multiplied to get -12?

Answer 8

to get -12?

Answer 9

Yeah?

Answer 10

ohhh, 4 x -3

Answer 11

i get it now

Answer 12

Its 12, and minus one, it has to also add up to -11

Answer 13

yup! okay, thank you!

Answer 14

Your welcome :), ill be here for a bit if you need anymore help

Answer 15

You can factor by grouping...
\[4y^2-11y-3=0\]
\[4y^2-12y+y-3=0\]
Remove a 3 from the first 2 terms.
\[4y(y-3)+(y-3)=0\]
Factor out a (y-3)
\[(y-3)(4y+1)=0\]
Easy to find the zeroes from here.

Answer 16

Remove a 4y from the first 2 terms***

Answer 17

Why do I have to remove a 4y from the first 2 terms? And why is it now (y-3)(4y + 1)?