Factor polynomials

Learning Objectives Factor polynomials by identifying and extracting the Greatest Common Factor (GCF). Apply special factoring formulas for difference of squares, sum of cubes, and difference of cubes. Factor polynomials with four terms using the grouping method. Factor higher-degree polynomials completely by applying multiple techniques in sequence. Use the Factor Theorem to identify linear factors of a polynomial. Solve polynomial equations by factoring and applying the Zero Product Property. How can we break down a complex mathematical expression into its simplest building blocks, just like a chemist identifies the elements in a compound? ⚛️ This tutorial will guide you through various techniques to factor polynomials. Mastering factoring is a critical skill in algebra,...

TermDefinitionExample PolynomialAn expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.5x^4 - 2x^3 + 8x - 1 is a polynomial. FactorA polynomial that divides another polynomial evenly, with no remainder.(x - 3) is a factor of x^2 - 9 because x^2 - 9 = (x - 3)(x + 3). Greatest Common Factor (GCF)The largest monomial that is a factor of each term of a given polynomial.The GCF of 12x^3y^2 + 18x^2y is 6x^2y. Prime PolynomialA polynomial with integer coefficients that cannot be factored into polynomials of a lower degree with integer coefficients.x^2 + 4 is a prime polynomial over the real numbers. Zero Product PropertyIf the product of two or more factors is zero, then...

Difference of Squares A^2 - B^2 = (A - B)(A + B) Use this when you have a binomial where both terms are perfect squares and they are separated by a subtraction sign. Sum of Cubes A^3 + B^3 = (A + B)(A^2 - AB + B^2) Use this for a binomial where both terms are perfect cubes and they are separated by an addition sign. Difference of Cubes A^3 - B^3 = (A - B)(A^2 + AB + B^2) Use this for a binomial where both terms are perfect cubes and they are separated by a subtraction sign.