Quadratics (a>1)
Factor:2x^2+7x+3
a*c = 6, factors: 6 & 1 Rewrite: 2x^2 + 6x+x+3 Group: 2x(x + 3) + 1(x + 3) → Answer: (2x+1)(x+3)
Factor:x^2-9
(x-3)(x+3)
Factor: x^3-8
a^3+b^3= (a-b)(a^2-ab+b^2)
Answer: a=x b=-2: (x-2)(x^2+2x+4)
Factor: x^3 + 3x^2 + x + 3
Group: (x^3 + 3x^2) + (x + 3) → x^2(x + 3) + 1(x + 3) → (x^2 + 1)(x + 3)
Factor:3x^2+10x+8
a*c = 24, Factors: 6 & 4 Rewrite: 3x^2+6x+4x+8 Group:3x(x+2) +4(x+2) Answer:(3x+4)(x+2)
Factor: 4x^2-25
(2x-5)(2x+5)
Factor: 27x^3-1
a^3-b^3 = (a-b)(a^2-ab+b^2)
a=3x b=-1 (3x-1)(9x^2+3x+1)
Factor: 2x^3 + x^2 + 6x + 3
(2x^3 + x^2) + (6x + 3) → x^2(2x + 1) + 3(2x + 1) → (x^2 + 3)(2x + 1)
Factor: 4x^2+12x+5
a*c = 20, Factors:10 & 2 Rewrite:4x^2+10x+2x+5 Group:2x(2x + 5)+1(2x + 5) Answer:(2x + 1)(2x + 5)
Factor:49x^2 - 1
(7x+1)(7x-1)
Factor: 64+x^3
a^3+b^3 = (a+b)(a^2-ab+b^2)
a=4 b=x (4-x)(16-4x+x^2)
Factor: x^3 - 2x^2 - x + 2
(x^3 - 2x^2) - (x - 2) → x^2(x - 2) -1(x - 2) → (x^2 - 1)(x - 2)
Factor:5x^2-13x+6
a*c =30,Factors:-10 &-3 Rewrite:5x^2-10x-3x+6 Group: 5x(x-2) -3(x-2) Answer: (5x-3)(x-2)
Factor:25x^2-36
(5x-6)(5x+6)
Factor: 125x^3+8
a^3+b^3 = (a+b)(a^2-ab+b^2)
a=5x b=2 (5x+2)(5x^2-10x+4)
Factor: 6x^3 + 3x^2 + 4x + 2
3x^2(2x + 1) + 2(2x + 1) → (3x^2 + 2)(2x + 1)
Factor: 6x^2+17x+5
a*c =30,Factors:15 & 2 Rewrite: 6x^2+15x+2x+5 Group: 3x(2x+5)+1(2x+5) Answer: (3x+1)(2x+5)
Factor:256x^2-961
(16x-31)(16x+31
Factor: 5832x^3+9261
a^3+b^3 = (a+b)(a^2-ab+b^2)
a=18x b=21 (18x+21)(324x^2-342+441)
Factor: x^3 - 5x^2 + 2x - 10
x^2(x - 5) + 2(x - 5) → (x^2 + 2)(x - 5