Directions on Factoring Polynomials
Polynomials are algebraic equations containing two squared or two cubed numbers. Each kind of polynomial equation contains one squared or cubed algebraic letter, i.e. x or y, and one squared or cubed number, such as 16, 49 or 125. To solve these equations, you must first factor them, or break them down into simpler pieces. After that, you solve them just like simple algebraic equations.
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Instructions
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Squared Polynomials
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Examine your polynomial equation. If it contains square roots, the equation contains subtraction. You cannot factor squared polynomials that are added.
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Find the square root of each squared number or letter in the equation. For instance, if your equation is y^2 -- 25, the square root of the first term is y and the square root of the second is 5.
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3
Split the equation into two equations in parentheses, one with a minus sign and one with a plus sign. The parentheses indicate multiplication of the two equations. In this case, the factored polynomial is (y+5)(y-5). Always place the equation with the plus sign first.
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Multiply the equation back together to check it. Multiply the first term in the first equation by all of the terms in the second equation. Multiply the second term in the first equation with the terms in the second equation. Add and subtract as the resulting equation requires; you should end up with your original equation if you've factored correctly.
Cubed Polynomials
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Examine your cubed polynomial. You may factor cubed polynomials whether the terms are added or subtracted. Just keep track of your signs; they are very important to factoring correctly.
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Find the cubed root of each term. For instance, x^3+y^3 has the cubed roots of x and y.
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Separate your cubed polynomial into one binomial (two term equation) and one trinomial (three term equation). For instance, the example would factor into (x+y)(x^2-xy+y^2). The binomial is always the cubed root of the two terms with the sign from the original polynomial. The trinomial is always the first term squared with the opposite sign (plus or minus) the two terms multiplied by each other, plus the second term squared.
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Note that if the original cubed polynomial is subtracted, the sign in the factored binomial will also be subtraction and both signs in the factored trinomial will be added. If the original cubed polynomial is added, the factored binomial will also be added. The first sign in the factored trinomial will be subtracted and the second sign will be added.
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Tips & Warnings
Remove any common factors that your terms share before doing any other factoring. For instance, if your original equation is 2x-4y, divide both terms by 2 before trying to do anything else. The resulting equation would be 2(y-2y) because you took a 2 away from each term.
References
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