Factor Polynomials By Grouping
1. Group a polynomial into two sides.
2. Take out the greatest common factor of each side.
3. Combine the factors and put them together with the remaining parts.
1. x3-x2-5x+5 --> (x3-x2)(-5x+5)
2. x2(x-1)-5(x-1)
3. (x2-5)(x-1)
Answer: (x2-5)(x-1)
1. Find out the square root of each part of the binomial.
2. Make the square roots together with one positive constant and one negative constant.
1. x2-4 --> x and 2
2. (x+2)(x-2)
Answer: (x+2)(x-2)
1. Split the middle part into 2 parts that can add up to the same but multiply to equal the last part of the problem.
2. Split the first digit into its square root and put it together with these two new parts.
1. x2+x-6 --> x2-2x+3x-6
2. (x-2)(x+3)
Answer: (x-2)(x+3)
Formula: a3+b3=(a+b)(a2-ab+b2)
1. determine a and b and insert into formula
1. a3+8 --> (a+2)(a2-2a+4)
Answer: (a+2)(a2-2a+4)
Formula: a3-b3=(a-b)(a2+ab+b2)
1. Determine a and b and insert into formula.
1. a3-8 --> (a-2)(a2+2a+4)
Answer: (a-2)(a2+2a+4)
x3+5x2-4x-20
(x2-4)(x+5)
x2-36
(x+6)(x-6)
x2+x-12
(x+4)(x-3)
27a3+512
(3a+8)(9a2-24a+64)
8a3-1000
(2a-10)(4a2+20a+100)
2x3-6x2+3x-9
(2x2+3)(x-3)
x4-144
(x2+12)(x2-12)
6x2+4x-10
(2x-2)(3x+5)
64a3+64
(4a+4)(16a2-16a+16)
125a3-125
(5a-5)(25a2+25b+25)
6n3+3n2+8n+4
(3n2+4)(2n+1)
x25-625
(x5+25)(x5-25)
2x2+9x-5
(2x-1)(x+5)
343a3+216
(7a+6)(49a2-42a+36)
729a3-1
(9a-1)(81a2+9a+1)