Home > Algebra calculators > Factoring Polynomials example

 Factoring Polynomials example ( Enter your problem ) FormulaExamples 2. Examples Type-1 (Taking common) Examples... (1) ax + a + 2x + 2 =(ax + a) + (2x + 2) =a(x + 1) + 2(x + 1) =(x + 1)(a + 2) Type-2 (Difference of squares) Examples... (1) 25x^2 - 36 =(5x)^2 - (6)^2 =(5x - 6)(5x + 6) Type-3 (Sum and Difference of cubes) Examples... (1) x^3 + 27 =(x)^3 + (3)^3 =(x + 3)(x^2 - (x)(3) + (3)^2) =(x + 3)(x^2 - 3x + 9) Type-4 (Whole square of a bionomial) Examples... (1) 4x^2 + 12xy + 9y^2 =(2x)^2 + 2(2x)(3y) + (3y)^2 =(2x + 3y)^2 Type-5 (Splitting the middle term of a Quadratic Equation) Examples... (1) x^2 + 10x + 24 =x^2 + 4x + 6x + 24 =x(x + 4) + 6(x + 4) =(x + 4)(x + 6) Type-6 (Whole square of a trinomial) Examples... (1) 4x^2 + y^2 + 1 + 4xy + 4x + 2y =(2x)^2 + (y)^2 + (1)^2 + 2(2x)(y) + 2(2x)(1) + 2(y)(1) =(2x + y + 1)^2 Type-7 (Factorization with the help of factor theorem) Examples... (1) x^3 - 3x^2 - 6x + 8 Here p(x)=x^3 - 3x^2 - 6x + 8 sum of coefficient of all the terms of p(x) = 1 - 3 - 6 + 8 = 0 :. (x-1) is a factor of p(x). Now, p(x) = x^3 - 3x^2 - 6x + 8 =x^3 - x^2 - 2x^2 + 2x - 8x + 8 =x^2(x - 1) - 2x(x - 1) - 8(x - 1) =(x - 1)(x^2 - 2x - 8) =(x - 1)(x - 4)(x + 2) Type-8 Cyclic Expressions Examples... (1) a^2(b - c) + b^2(c - a) + c^2(a - b) = a^2b - a^2c + b^2c - b^2a + c^2a - c^2b = a^2b - a^2c + cb^2 - ab^2 + ac^2 - bc^2 = a^2b - a^2c - ab^2 + ac^2 + b^2c - bc^2 = a^2(b - c) - a(b^2 + c^2) + bc(b - c) = a^2(b - c) - a(b - c)(b + c) + bc(b - c) = (b - c)(a^2 - a(b + c) + bc) = (b - c)(a^2 - ab - ac + bc) = (b - c)(a(a - b) - c(a - b)) = (b - c)(a - b)(a - c) = -(a - b)(b - c)(c - a) This material is intended as a summary. Use your textbook for detail explanation.Any bug, improvement, feedback then Submit Here