1 Get all the terms on the same side. Before you can solve a polynomial equation, you have zero on one side of the equation and everything else on the other. Fortunately, you can use addition or
subtraction to move things around. For example, if you have the equation x^2 + 2x = 8, you can subtract 8 from both sides: x^2 +2x = 8x^2 + 2x -8 = 8 -8x^2 +2x -8 = 0
2 Factor out any number you can. If a number is a factor of all the terms in the equation, you can factor it out. For example, in 4y^2 +8y + 6 = 0 , 2 is a factor of everything, since all three terms on the left side can be divided by two. Factoring it out, we get: 4y^2 8y +6 = 02(2y^2 + 4y +3) = 0
3 Factor out any common variables. If every term in your polynomial has a variable in it, you can factor it out just like a number. For example, in the polynomial 3a^2 +a = 0 , both terms have an "a" in them: 3a^2 +a = 0a(3a +1) = 0
4 Factor any remaining complex terms. For example, once you factor out the number "2" from 2x^2 - 2 = 0, you are left with 2(x^2 -1) = 0. You can factor this one step further: 2(x^2 -1) = 02(x+1)(x - 1) = 0 See the link below to learn more about factoring polynomials.
5 Solve the equation. Once the left side is factored out, you can get a solution by noticing that every part with a variable is equal to zero. For example, in 2(x + 1)(x - 1) = 0, both x + 1 and x - 1 are equal to zero. You can get two solutions by just plugging in the numbers:First Solutionx + 1 = 0x + 1 - 1 = 0 - 1x = -1 Second Solution x - 1 = 0 x - 1 + 1 = 0 + 1x = 1
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