How do you factor 5y^2-3y-25y2−3y−2?

1 Answer
Don't Memorise
Aug 10, 2015

= color(blue)((5y+2)(y-1) =(5y+2)(y−1)

Explanation:

5y^2−3y-25y2−3y−2

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like ay^2 + by + cay2+by+c, we need to think of 2 numbers such that:

N_1*N_2 = a*c = 5*-2 = -10N1⋅N2=a⋅c=5⋅−2=−10
and,
N_1 +N_2 = b = -3N1+N2=b=−3

After trying out a few numbers we get N_1 = -5N1=−5 and N_2 =2N2=2
-5*2 = -10−5⋅2=−10, and 2+(-5)=-32+(−5)=−3

5y^2−color(blue)(3y)-2 = 5y^2−color(blue)(5y+2y)-25y2−3y−2=5y2−5y+2y−2

= 5y(y-1) +2(y-1)=5y(y−1)+2(y−1)

= color(blue)((5y+2)(y-1) =(5y+2)(y−1)

Related questions
See all questions in Factoring Completely
Impact of this question
2166 views around the world
You can reuse this answer
Creative Commons License