Question

Factor the expression y2+6y-16

Answer 1

Step 1 ) Break up the expression.

$\displaystyle\ y^{2} + 6y -16$

$\displaystyle\ (y^{2} -2y) + (8y -16)$

Step 2 ) Factor y from $y^{2} - 2y$.

$\displaystyle\ (y^{2} -2y) + (8y -16)$

$\displaystyle\ y ( y - 2 )$

Step 3 ) Factor 8 from $8y - 16$

$\displaystyle\ (y^{2} -2y) + (8y -16)$

$\displaystyle\ 8 ( y - 2)$

Step 4 ) Place new factors in group.

$\displaystyle\ y ( y - 2 )$

$\displaystyle\ 8 ( y - 2)$

$\displaystyle\ y(y-2)+8(y-2)$

Step 5 ) Distribute.

$\displaystyle\ y(y-2)+8(y-2)$

$\displaystyle\ (y-2) + 8(y-2)$

$\displaystyle\ (y-2) (y+8)$

The expression factored is...

$\framebox {=(y-2)(y+8)}$

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- Marlon Nunez

Answer 2

$y^2+6y-16=y^2+8y-2y-16=y(y+8)-2(y+8)=(y+8)(y-2)$