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**Factoring – Trinomials (a ≠ 1),**

Bottoms Up Method This is the third method shown for factoring The two previous methods shown were Guess and Check ac. You only need to know one of the three methods! Bottoms Up will be explained using an example.

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Example 1 Factor: Determine the value of ac. Write a trinomial in the form of x2+bx+ac. We already know how to factor trinomials of this form.

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**Since b=17 is positive, let the negative factor be**

the smaller of the two numerical values. Factors of -60 Sum of Factors

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

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

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**The trinomial is factored using**

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Example 2 Factor: Determine the value of ac Write a trinomial in the form of x2+bx+ac.

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**To multiply and get 420 which is positive, the**

factors will need to be the same sign. To add to -43 means they will both be negative. Factors of 420 Sum of Factors Start with larger numbers since we know (-1)(-420) won’t even be close.

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

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

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**The trinomial is factored using**

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Example 3 Factor: Determine the value of ac Write a trinomial in the form of x2+bx+ac.

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

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

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**This is not the same as the original trinomial!**

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: Factor the GCF Now factor the trinomial factor Determine the value of ac Write a trinomial in the form of x2+bx+ac.

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

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

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**Back to the original where we took out the GCF.**

Write in the binomial factors.

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**The trinomial is factored using**

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END OF PRESENTATION

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