How to Factor Polynomials As Perfect Squares
Factoring is a process taught in algebra that helps students simplify seemingly complicated algebraic expressions. When your algebraic expression meets certain qualifications, you can take a shortcut when factoring known as factoring a perfect square trinomial. To use this method, the first and last terms must be perfect squares, and the middle term must equal double the product of the square roots.
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Instructions
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1
Arrange your polynomial into the form ax^2 + bx + c. For example, if you had 25 - 10x +x^2, you would rearrange it to read x^2 - 10x + 25.
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2
Take the square root of the first term in the polynomial. In this example, you would take the square root of x^2 and get x.
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3
Take the square root of the last term in the polynomial. In this example, you would take the square root of 25 and get 5.
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4
Multiply the result from step 2 times the result from step 3 times 2. Continuing the example, you would multiply x times 5 times 2, and get 10x.
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5
Compare the result from step 4 to the middle term in your polynomial, disregarding the plus or minus in front of the second term. If they are not equivalent, stop. You cannot factor this expression as a perfect square. If they are equivalent, continue. In this example, the 10x from step 4 equals the 10x from the polynomial, so you can continue.
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6
Write the factored version of the polynomial in the form (d +/- e)^2, where d is the result from step 2, e is the result from step 3 and the plus or minus is determined by the sign of the second term in the polynomial. Finishing the example, you would put in x for d, 5 for e and a minus sign because the original polynomial, x^2-10x+25, had a minus sign before the second term, which makes your factored expression (x-5)^2.
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Tips & Warnings
The polynomial must match the formula exactly; otherwise, you will not be able to use the perfect squares method of factoring.
References
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