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Published byHannah Hodge Modified over 9 years ago
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Long Division of Polynomials A different way to factor (7.5)
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SAT Prep Quick poll! 1.
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SAT Prep Quick poll! 2.
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SAT Prep Quick poll! 3.
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POD Factor: x 2 – x – 12 Can you use that pattern to factor this one completely? x 4 – x 2 – 12
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Pattern review Difference of squares: a 2 – b 2 = (a + b)(a - b) Difference of cubes: a 3 – b 3 = (a - b)(a 2 + ab + b 2 ) Sum of cubes: a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Factoring by grouping (split the middle term) If the discriminant is a perfect square, then the quadratic trinomial can be factored.
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Factoring and division If then So, what is ? What are the remainders with these? What does that mean?
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Division with a remainder We can divide polynomials, even if we get a remainder that isn’t zero. In that case, we don’t factor, but do something called long division of polynomials. It’s a lot like long division of numbers.
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Division with a remainder First, let’s review the following terms, and do a simple long division problem. dividend divisor remainder quotient
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Division with a remainder Here’s how it works for polynomials. becomes The tricky part to keep straight is what is positive and negative. A remainder of 0 means we have factors.
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Try another Use the same technique here.
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Try another This time the divisor is not linear, but the process is the same.
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Try another You may find this result familiar.
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A shortcut When the divisor is linear, we can use something called synthetic division to find a quick answer. What was our answer before? How does it compare to these numbers?
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Shortcut again Try it with this one. Watch for spacers!
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