Question

Find the binomial factors of the equation

Answer 1

is it (y-3) (y-5) ?1

Answer 2

Let's find out!

\[(y-3)(y-5) = y(y-5)-3(y-5) = y^2 - 5y -3y + 15 = y^2-8y+15\]Sadly, that is not what we started with.

Answer 3

hmmm

Answer 4

Here's how to work it:

We know that if we multiply two binomials:\[(x+a)(x+b) = x^2 + ax + bx + ab\]or\[x^2+(a+b)x + ab\]Let's compare that with your trinomial (I'm changing to x because that's what I type all the time!):
\[x^2+(a+b)x + ab\]\[x^2-2x-35\]
We can make those equal to each other so long as \((a+b) = -2\) and \(ab = -35\), right?

Answer 5

So, our job is to pick two numbers which are factors of -35, and which add to -2. Can you think of two such numbers? Obviously, one will be positive and the other negative.

Answer 6

yeah (y-7) (y+5) , right?

Answer 7

Correctamundo!