\( \begin{array}{ll}\text { 2. } & x^{2}-7 x+12 \\ \text { 4. } & x^{2}-x-12 \\ \text { 6. } & 5 a^{2}+35 a-40 \\ \text { 8. } & 3 y^{2}+9 y+6 \\ \text { 10. } & 2 x^{2}-24 x+70\end{array} \)

Factor the expression by following steps: - step0: Factor: \(x^{2}-x-12\) - step1: Rewrite the expression: \(x^{2}+\left(3-4\right)x-12\) - step2: Rewrite the expression: \(x^{2}+3x-4x-12\) - step3: Factor the expression: \(x\left(x+3\right)-4\left(x+3\right)\) - step4: Factor the expression: \(\left(x-4\right)\left(x+3\right)\) Factor the expression \( 3 y^{2}+9 y+6 \). Factor the expression by following steps: - step0: Factor: \(3y^{2}+9y+6\) - step1: Factor the expression: \(3\left(y^{2}+2y+y+2\right)\) - step2: Factor the expression: \(3\left(y\left(y+2\right)+y+2\right)\) - step3: Factor the expression: \(3\left(y+1\right)\left(y+2\right)\) Factor the expression \( x^{2}-7 x+12 \). Factor the expression by following steps: - step0: Factor: \(x^{2}-7x+12\) - step1: Rewrite the expression: \(x^{2}+\left(-3-4\right)x+12\) - step2: Rewrite the expression: \(x^{2}-3x-4x+12\) - step3: Factor the expression: \(x\left(x-3\right)-4\left(x-3\right)\) - step4: Factor the expression: \(\left(x-4\right)\left(x-3\right)\) Factor the expression \( 5 a^{2}+35 a-40 \). Factor the expression by following steps: - step0: Factor: \(5a^{2}+35a-40\) - step1: Factor the expression: \(5\left(a^{2}+8a-a-8\right)\) - step2: Factor the expression: \(5\left(a\left(a+8\right)-\left(a+8\right)\right)\) - step3: Factor the expression: \(5\left(a-1\right)\left(a+8\right)\) Factor the expression \( 2 x^{2}-24 x+70 \). Factor the expression by following steps: - step0: Factor: \(2x^{2}-24x+70\) - step1: Factor the expression: \(2\left(x^{2}-5x-7x+35\right)\) - step2: Factor the expression: \(2\left(x\left(x-5\right)-7\left(x-5\right)\right)\) - step3: Factor the expression: \(2\left(x-7\right)\left(x-5\right)\) Here are the factored forms of the given expressions: 1. For \( x^{2}-7x+12 \): \[ x^{2}-7x+12 = (x-4)(x-3) \] 2. For \( x^{2}-x-12 \): \[ x^{2}-x-12 = (x-4)(x+3) \] 3. For \( 5a^{2}+35a-40 \): \[ 5a^{2}+35a-40 = 5(a-1)(a+8) \] 4. For \( 3y^{2}+9y+6 \): \[ 3y^{2}+9y+6 = 3(y+1)(y+2) \] 5. For \( 2x^{2}-24x+70 \): \[ 2x^{2}-24x+70 = 2(x-7)(x-5) \] If you need further assistance or explanations, feel free to ask!