How do you factor the expression #-y^2 + 9y - 20#?

Question

Eva Abramson · Accepted Answer

#-(y- 4)(y - 5) = (4 - y)(y - 5) = (y - 4)(5 - 4)#

It is very uncomfortable working with a negative sign in the first term. Swopping the first and third terms will not help.

Divide out the negative. (actually -1), causing the signs in the bracket to change.

#-(y^2 - 9y + 20)#

Finding factors of 20 which add to 9 leads to 4 and 5. The signs in the brackets will be the same (because of the +20), both signs will be negative (because of the -9).

This gives #-(y- 4)(y - 5)#

It can be left like this or multiplying the negative into either one of the brackets gives #(4 - y)(y - 5) or (y - 4)(5 - 4)#

Eva Adamson · Answer

undefined To factor the expression $ -y^2 + 9y - 20 $, first, look for two numbers that multiply to give the product of the leading coefficient (-1) and the constant term (-20), which is -20. These numbers should also add up to the middle coefficient, which is 9. The numbers that fit these criteria are 4 and -5.

Now, rewrite the middle term using these two numbers:
$$ -y^2 + 4y - 5y - 20 $$

Next, factor by grouping:
$$ (-y^2 + 4y) + (-5y - 20) $$

Factor out the greatest common factor from each pair of terms:
$$ -y(y - 4) - 5(y - 4) $$

Now, notice that both terms have a common factor of $ (y - 4) $:
$$ (y - 4)(-y - 5) $$

So, the factored form of $ -y^2 + 9y - 20 $ is $ (y - 4)(-y - 5) $.