Question

Which equation could be used to solve y 2+7y=18 by factoring?

y(y + 7) = 18
(y + 2)(y + 9) = 0
(y + 9)(y - 2) = 0

Answer 1

@whpalmer4 Are you free for a minute?

Answer 2

\[y^2+7y=18\]If we subtract 18 from both sides, we have
\[y^2+7y-18=0\]

To factor that, we'll end up with a pair of binomials of the form \[(x+a)(x+b) = x^2 + ax + bx + ab \]\[=x^2 + (a+b)x + ab\]Comparing that with the original, \[y^2+7y-18\]we see that we need to find two numbers \(a,b\) such that \[a+b=7\]\[a*b=-18\]

To get a negative product without involving imaginary numbers, we'll have to have one positive factor and one negative factor of -18, and they'll have to add to 7. Can you figure out what they would be?

Answer 3

-18 = -1*18, -2*9, -3*6, -6*3, -9*2, -18*1

Answer 4

Oh yeah ok so i am with you so far

Answer 5

Okay, so which pair of factors will we use?

Answer 6

Does it matter which one??

Answer 7

yes! didn't you read my 1st post?

Answer 8

Ok in that case im lost lol

Answer 9

Look, we're trying to find the two binomials that we multiply together to get \(y^2-7y-18\)
They will be of the form \((y+a)(y+b)\) where \(a\) and \(b\) are numbers we need to find.

Now, when we multiply \[(y+a)(y+b) = y(y+b) + a(y+b) = y^2 + (a+b)y + ab\]we can see that for our factoring to work, we have to pick two numbers \(a,b\) so that \[(a+b)y = -7y\]divide both sides by \(y\)\[a+b=-7\]
and \[a*b = -18\]

Answer 10

OH! Now i see why i need to have a specific number.

Answer 11

So, your choices:

-1*18
-2*9
-3*6
-6*3
-9*2
-18*1

which of those pairs will multiply to -18 (all of them) and sum to 7 (only one of them)?

That will give you your factoring: (y+a)(y+b) (one of them will be negative, so it will be a - instead of a plus)

Answer 12

I have to go, hopefully you've grasped the idea here...

Answer 13

Yes thank you. I have enough to figure it out from here :)