How to Check Your Answer When You Factor a Polynomial
Factoring simplifies a polynomial by splitting the polynomial up into its multiples. Factoring can be achieved by finding the greatest common factor of the polynomial's segments and/or by grouping. Checking your work is a vital part of factoring as the slightest mistake, such as a plus sign instead of a minus sign, can completely change the expression. Checking your answer is as simple as working the problem back in reverse until you get back to the original quantity.
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Instructions
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Factor the polynomial 2x^2y + 18xy + 36y and check your work. Begin by pulling the greatest common factor (GCF) out of the polynomial. Pull the "2y" out of each of the values: 2y (x^2 + 9x + 18).
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Factor the expression left in the parentheses by grouping. Set it up as 2y ( )( ), with the blanks left inside for the numbers you're about to find. Look at the expression "x^2 + 9x + 18" and decide what needs to be done to create the "x^2". Fill in the parentheses accordingly: 2y (x )(x ).
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Determine what numbers can finish out the parentheses and create the "9x" and "18". Note that 6 + 3 = 9 and 6 * 3 = 18. Fill in the parentheses: 2y (x + 6)(x + 3).
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Check your answer by multiplying the expression through. Begin by multiplying out the "(x + 6)" and "(x + 3)": x * x + x * 3 + 6 * x + 6 * 3 = x^2 + 3x + 6x + 18 = x^2 + 9x +18. Multiply this answer through by "2y": 2y (x^2 + 9x + 18) = 2x^2y + 18xy + 36y. Confirm that this matches the original expression.
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