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# Algebra

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The expression 3y^2-y-24+10 can be written as (3y + a)(y + b), where a and b are integers. What is a-b?

May 8, 2022

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Note that $$3y^2 - y - 24 + 10 = 3y^2 - y - 14$$.

Then, note that -y = 6y - 7y, so we have:

$$\begin{array}{cl} & 3y^2 - y - 14\\ =& 3y^2 + 6y - 7y - 14\\ =& 3y(y + 2) - 7(y + 2) \end{array}$$

Now you can take out the common factor (y + 2) and compare with what the question gave you. Can you proceed from here?

May 8, 2022