Factor -y^2+y+30

Question

This is a factoring question that I have difficulty on

Answer 1

Hello Naren,

 

When the squared term has a negative, I find it best to factor a -1 from everything before beginning:

-y²+y+30

= -1(y²-1y-30).  Now look for two numbers which multiply to -30, but add to -1.

*Note the -1 about which I am speaking now, is the coefficient of the y-term*

 

So we want -6 and +5, since (-6)(+5) = -30 and -6+(+5) = -1, which gives us:

 

-1(y-6)(y+5)

 

Thank you for posting the question!

Michael Ehlers

Answer 2

Let's first factor out the negative. That way it looks much more like a standard quadratic:

-(y² - y - 30)

What we need next is two numbers that multiply together equal -30, and when added together we get -1.

5 * 6 = 30 we know from our multiplication tables. If we add a negative sign to one of numbers, we get -30:

5 * -6 = -30

Additionally:

5 - 6 = -1

 

So that means this quadratic factors into:

-(y + 5)(y - 6)