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Published byZoe Scoble Modified about 1 year ago

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Factoring – Trinomials (a ≠ 1), Bottoms Up Method You only need to know one of the three methods! The two previous methods shown were 1.Guess and Check 2.ac. This is the third method shown for factoring Bottoms Up will be explained using an example.

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Example 1 Factor: 1.Determine the value of ac. 2.Write a trinomial in the form of x 2 +bx+ac. We already know how to factor trinomials of this form.

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Sum of FactorsFactors of -60 Since b=17 is positive, let the negative factor be the smaller of the two numerical values.

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3.Write two factors using the two numbers. 4.Divide the two numbers by the value of a in the original trinomial.

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5.Reduce the fractions. 6.Complete using the “bottoms up” step

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The trinomial is factored using

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Example 2 Factor: 1.Determine the value of ac 2.Write a trinomial in the form of x 2 +bx+ac.

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To multiply and get 420 which is positive, the factors will need to be the same sign. Sum of FactorsFactors of 420 To add to -43 means they will both be negative. Start with larger numbers since we know (-1)(-420) won’t even be close.

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3.Write two factors using the two numbers. 4.Divide the two numbers by the value of a in the original trinomial.

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5.Reduce the fractions. 6.Complete using the “bottoms up” step

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The trinomial is factored using

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Example 3 Factor: 1.Determine the value of ac 2.Write a trinomial in the form of x 2 +bx+ac.

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3.Factor 4.Divide the two numbers by the value of a in the original trinomial.

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5.Reduce the fractions. 6.Complete using the “bottoms up” step

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Do you see the error? This is not the same as the original trinomial!

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Note that the original trinomial has a common factor. IMPORTANT: you must factor the GCF before using Bottoms Up. Let’s redo the problem.

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Factor: 1.Determine the value of ac 2.Write a trinomial in the form of x 2 +bx+ac. Factor the GCF Now factor the trinomial factor

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3.Factor 4.Divide the two numbers by the value of a in the original trinomial.

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5.Reduce the fractions. 6.Complete using the “bottoms up” step

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7.Back to the original where we took out the GCF. 8.Write in the binomial factors.

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The trinomial is factored using

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