Solving Equations by Factoring Practice

Make one side equal to 0.

\(y^3+5y^2+20y \color{red}{+2y^2-8y}=-2y^2+8y \color{red}{+2y^2-8y} \\ \, \\ y^3+7y^2+12y=0 \\ \, \\ \underbrace{y^3+7y^2+12y}_{\text{Factor y} } =0 \\ \, \\= (y)(y^2+7y+12) \\ \, \\= (y)\underbrace{(y^2+7y+12)}_{\text{Factorize}} \\ \, \\= (y)(y+3)(y+4) \\ \, \\\)

Make one side equal to 0.

\(-2x^3+30x \color{red}{+4x^2}= -4x^2\color{red}{+4x^2} \\ \, \\ -2x^3+4x^2+30x=0 \\ \, \\ \underbrace{-2x^3+4x^2+30x}_{\text{Factor } -2x} =0 \\ \, \\= (-2x)(x^2-2x-15) \\ \, \\= (-2x)\underbrace{(x^2-2x-15)}_{\text{Factorize}} \\ \, \\= (-2x)(x-5)(x+3) \\ \, \\\)

Make one side equal to 0.
\(x^2-11x-2 \color{red}{+30}=-30\color{red}{+30} \\ \, \\ x^2-11x+28=0 \\ \, \\ \underbrace{x^2-11x+28}_{\text{Factorize }} =0 \\ \, \\= (x-7)(x-4) \\ \, \\ \)