A-Ch4b-Factoring

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DCubes: 8x³-27y³

(2x-3y)(4x²+6xy+9y²)

Tri: 3x²+7x+2

(3x+1)(x+2)

SCubes: 27x³+125y³

(3x+5y)(9x²-15xy+25y²)

Tri: 12x²-5x-2

(4x+1)(3x-2)

SCubes: 125x³+216y³

(5x+6y)(25x²-30xy+36y²)

DS: x²-25

(x+5)(x-5)

Tri: x²+6xy-16y²

(x+8y)(x-2y)

DS: x²-y²

(x+y)(x-y)

SCubes: x³+y³

(x+y)(x²-xy+y²)

SCubes: x³+y^6

(x+y²)(x²-xy²+y^4) [any exponent that is a multiple of 3 is a perfect cube]

Tri: x²-5x+6

(x-2)(x-3)

DCubes: x³-8

(x-2)(x²+2x+4)

DCubes: x³-y³

(x-y)(x²+xy+y²) [find the cube root for first set of parenthesis]

DS: x^4 -1

(x²+1)(x²-1) [1 is still a perfect sqaure] --> (x²+1)(x+1)(x-1)

DS: x^4 -36

(x²+6)(x²-6) [any even exponent is a perfect square]

DS: x^4 -81

(x²+9)(x²-9) [9 is still a perfect sqaure] --> (x²+9)(x+3)(x-3)

DS: x^6 -64

(x³+8)(x³-8) [any even exponent is a perfect square]

Grouping: 10m+2n+5mk+nk

2(5m+n) +k(5m+n) THEN --> (5m+n)(2+k)

Grouping: 6x²-4x-15x+10

2x(3x-2) -5(3x-2) THEN --> (3x-2)(2x-5)

Grouping: 3x-3y+ax-ay

3(x-y) +a(x-y) THEN factor out (x-y) to get answer--> (x-y)(3+a)

GCF: 9x-18

9(x-2) [divide out the common 9 from each term and place it on the outside of parenthesis]

Solve by Factoring

First factor then set each factor = to zero and solve for variable to find solution(s)

Tri: ax²+bx-c

If last sign is a negative Factor using + - --> (?+?)(?-?)

Tri: ax²-bx-c

If last sign is a negative Factor using + - --> (?+?)(?-?)

Tri: ax²+bx+c

If last sign is a plus Factor using 2 of the middle term's sign --> (?+?)(?+?)

Tri: ax²-bx+c

If last sign is a plus Factor using 2 of the middle term's sign --> (?-?)(?-?)


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