A-Ch4b-Factoring
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 --> (?-?)(?-?)
