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## Factoring by GCF - Greatest Common Factor ### Examples 1. $6x^2 + 15x^4$ - GCF: $3x^2$ - Factors: $3x^2(2+5x)$ 2. $7y - 63y^2$ - GCF: $7y$ - Factors: $7y(1-9y)$ 3. $69(z^2-3)$ - GCF: $69$ - Factors: $69(z-3)$ ## Factoring Perfect Square Trinomial ### Square of a binomi...

## Factoring by GCF - Greatest Common Factor ### Examples 1. $6x^2 + 15x^4$ - GCF: $3x^2$ - Factors: $3x^2(2+5x)$ 2. $7y - 63y^2$ - GCF: $7y$ - Factors: $7y(1-9y)$ 3. $69(z^2-3)$ - GCF: $69$ - Factors: $69(z-3)$ ## Factoring Perfect Square Trinomial ### Square of a binomial **Ex:** $\sqrt{x^2+2x+1}$ $\rightarrow$ $(x+1)(x+1)$ $\rightarrow$ $(x+1)^2$ ### Examples 1. $y^2 + 10y + 25$ $\rightarrow$ $(y+5)(y+5)$ $\rightarrow$ $(y+5)^2$ 2. $6z^2 - 6z + 9$ $\rightarrow$ $(6z-3)(6z-3)$ $\rightarrow$ $(6z-3)^2$ 3. $4x^2 - 12x+ 9$ $\rightarrow$ $(2x-3)(2x-3)$ $\rightarrow$ $(2x-3)^2$ 4. $25k^2 + 50k + 4$ $\rightarrow$ $(5k+2)(5k+2)$ $\rightarrow$ $(5k+2)^2$ ## General Trinomial of the form $x^2 - bx + c$ ### Examples 1. $x^2 + 10x + 25$ $\rightarrow$ $(x+5)(x+5)$ 2. $y^2-7y+b$ $\rightarrow (y-5)(y-2)$ 3. $3m^2-27m-90$ $\rightarrow (m-30)(m+3)$