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You might be wondering where the 30 and the 11 come from in the number puzzle.
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Well we actually multiply the coefficient of the x squared term and the constant
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term together to get this top number. This bottom number 11 comes from our x
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term. Whenever we want to factor a trinomial we can set up a number puzzle and
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then find the two factors we need to rewrite the x term. So, I can rewrite this
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expression as x squared plus 5x plus 6x plus 30. We can rewrite the 11x as 5x
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and 6x. The 2 numbers come from our number puzzle. By rewriting this x term as
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5x plus 6x we can use factoring by grouping. I remove an x from the first 2
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terms and a six from the second two terms. And whoa, look at that, our factored
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form. So for any quadratic trinomial, we can try this process to factor it. We
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can find two factors of a times c, that sum to the middle number b. We'll
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rewrite the middle term using those factors and then try factoring by grouping.