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**Dividing Polynomials 3π₯+5 π₯+2 | 3 π₯ 2 +11π₯+10 Quotient Divisor**

π₯+2 | 3 π₯ 2 +11π₯+10 Quotient Divisor Dividend

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Divide 2466 7

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**Dividing Polynomials π₯ 2 +3π₯ β 8 π₯+2 Long division**

Write as a long division problem. Focusing on the front term, figure out what you need to multiply by to get the first term of the polynomial Write that on top of the βhouseβ and multiply it through to the divisor Subtract the resulting expression Repeat the process until you get to the end of the dividend If there is a remainder, write that as a fraction. π₯ 2 +3π₯ β 8 π₯+2

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You Try: 4 π₯ 2 β5π₯+8 π₯ ) 3 π₯ 2 β7π₯+12 π₯ β5

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**This can ONLY be done when divisor is x Β± c**

Dividing Polynomials synthetic division This can ONLY be done when divisor is x Β± c Write the OPPOSITE of the divisorβs constant on the outside of a vertical line | Write the COEFFICIENTS of the dividend next to that (keep the signs) Drop the first dividend number, multiply that by the divisor number and place under the next coefficient Add the two numbers and write the result under that, repeat the process of multiplying and adding until you get to the end of the polynomial Write the results as the quotient, the last value is the remainder. π₯ 2 +3π₯ β4 π₯+2

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You Try: 7 π₯ 2 β6π₯+1 π₯ β3 2) 8 π₯ 2 β12π₯ β17 π₯+7

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**Also, x β a is a FACTOR of p(x) if f(a) = 0**

Remainder Theorem: For a given a polynomial, p(x), the remainder when dividing by x β a [a is a constant] will be equal to p(a). [the value of the polynomial when you substitute a in for x] Also, x β a is a FACTOR of p(x) if f(a) = 0 [remainder is zero] Example: Determine if x + 2 is a FACTOR of 2x2 β 3x + 5.

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