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We can make a table to list of all the ways we can multiply to get –12 and check to see if the sum is –1: Step 2: We need to find two numbers that multiply (product) to give you –12 and add (sum) to give you –1. Factor a Trinomial (No Fuss Factoring Method) Of the terms in the first parentheses and the sign will be the opposite of that in the first parentheses.Ĩp 3 – 27 = ( 2p ) 3 – (3) 3 = ( 2p – 3 )[( 2p ) 2 + ( 2 p In the second parentheses, the first term will be the same as the first term in the first parentheses squared; the last term will be the same as the last term in the first parentheses squared; the middle term will be the product In the first set of parentheses, we include one factor of each cubed term and the sign will be the same as that of the original problem.
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In order to do so, we open two sets of parentheses. This means we can use the difference of cubes formula to factor this problem. Notice in this example that we have the subtraction of two terms where both terms are perfect cubes: 8p 3 = (2p) 3 and 27 = (3) 3. Next we include in one parenthesis a “+” sign and a “–” sign in the other.Ħ4p 2 – 9n 2 = ( 8p ) 2 – (3n) 2 = ( 8m + 3n )(8m – 3n) = ( 8m + 3n)(8m – 3n). In order to do so, we open two sets of parenthesis and include in each parenthesis one factor of each squared term. This means we can use the difference of squares formula to factor this problem. Notice in this example that we have the subtraction of two terms where both terms are perfect squares:Ħ4p 2 = ( 8p ) 2 = (8p)(8p) and 9n 2 = (3n) 2= (3n)(3n). This means we can factor out (or divide) 4mp from each term in the polynomial.Ĩm 2p 2 + 4mp = (4mp)(2mp) + (4mp)(1) = 4mp(2mp + 1) Notice in this example that there is a GCF of 4mp. This means we can factor out (or divide) 9 from each term in the polynomial. Notice in this example that there is a GCF of 9. Step 3: Check the factored form by multiplying. If the polynomial has more than three terms, try to factor by grouping. If it is not, then try factoring using the AC Method. If the polynomial is a trinomial, check to see if it is a perfect square trinomial. Step 2: If the polynomial is a binomial, check to see if it is the difference of squares, the difference of cubes, or the sum of cubes.
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Step 1: Factor out any common factors (GCF).
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