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Factoring Polynomials How to Factor Trinomials in the form of ax2 + bx + c Step 1: Are there any common factors? If so, factor them out. Step 2: How many terms are in the polynomial? A. If there are Two terms, decide if one of the following can be applied 1. Difference of two Squares: 2. Difference of two Cubes: 3. Sum of two cubes: B. C. If there are Three terms, try one of the following. 1. Perfect Square Trinomial a2 + 2ab + b2 = (a + b)2 2. Perfect Square Trinomial a2 − 2ab + b2 = (a − b)2 3. If not a perfect square trinomial, then try using the Fraction Method If there are Four terms, try factoring by grouping. Factoring Trinomials in the form of ax2 + bx + c Fraction Method EXAMPLE: 2 x 9 x 18 2 Step 1: Copy the trinomial into an expression: a fraction with two binomials with the leading coefficient in both quantities divided by that coefficient: (2 x )(2x ) 2 Step 2: Multiply the leading coefficients by the last number in the trinomial: 2 X 18 = 36 Step 3: Find Factors of 36 that yield the middle value when added or subtracted. Hint! The last sign tells us to subtract the factors. ___________ 36________ In this example the two factors are 3 and ‐12 1 36, 2 18, 3 12, 4 9, 6.6, Step 4: The two factors are substituted into the original expression: (2 x -12)(2x 3) Step 5: Factor the common number(s) and reduce the numbers: 2( x 6)(2 x 3) 2 2 Step 6: The remaining factors are the answer to the trinomial factorization: ( x 6)(2 x 3) Step 7: Check! Multiply the binomials. If your factors are correct, you should get the original trinomial. Foil ( x 6)(2 x 3) 2 x 2 3 x 12 x 18 2 x 2 9 x 18 saved: Math Handout (Factoring) 2 1