The expression 3y^2 - y - 24 - 21y + 8 can be written as (3y+a)(y+b) where a and b are integers. What is a-b ?

Guest Feb 18, 2022

#1**0 **

Simplify the expression: \(3y^2-22y-16\)

In order to fractor this quadratic, we need to break up the -22 to 2 numbers which multiply to -48, and add to -22.

Looking through the list of factor pairs of -48, we find that -24 and 2 satisfy both conditions.

Rewrite as: \(3y^2-24y+2y-16\)

Factor: \(3y(y-8) + 2(y-8)\)

Rewrite again: \((3y+2)(y-8)\)

From here, you know what \(a\) and \(b\) are, and you can solve for \(a-b\)

BuilderBoi Feb 18, 2022