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Step 1
Write your trinomial in standard form. Choose one variable and list that variable’s terms in descending order of degree (i.e., start with the term that has the largest exponent). Do it like this:a(x squared) + bxy + c(y squared)ora(x squared) + bx + c
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Step 2
Multiply the first and last coefficients (a * c or ac).
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Step 3
List the factors of the product.F * f = ac
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Step 4
Look over the factor pairs as you list them and choose a pair (F, f) whose sum is b.F + f = b
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Step 5
Express the middle term (bxy) of the trinomial as a sum using the factor pair you choose as the coefficients.Fxy + fxy = bxy
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Step 6
Substitute back into your original trinomial: a(x squared) + Fxy + fxy + c (y squared). Make two groups and factor out the greatest common factor of each group. Look for a common factor of your new products and factor it out.
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Step 7
Check your answer.An example will show how easy this method really is:12(x squared) + 17x + 6The product of ac is 72 (12 * 6).Begin listing the factors of 72:2 363 244 186 128 9Stop at this point, because you realize that the sum of this factor pair is b: (8 + 9 = 17).Rewrite the original trinomial using this factor pair to form the middle term:12x-squared + 8x + 9x + 6Make two groups:(12x-squared + 9x) + (8x + 6) *Note the advantageous grouping.Factor3x(4x + 3) + 2(4x + 3)Look for a common factor (4x + 3) in the two new products and factor it out.(3x+ 2)(4x + 3)Check by multiplying(3x+ 2)(4x + 3) = 12x-squared + 9x + 8x + 6 = 12(x squared) + 17x + 6
