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**Section 3 Dividing Polynomials**

Chapter 6 Section 3 Dividing Polynomials

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**Long Division Vocabulary Reminders**

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**Remember Long Division**

Does 8 go into 6? No Does 8 go into 64? Yes, write the integer on top. Multiply 8∙8 Write under the dividend Subtract and Carry Down How many times does 8 go into 7 evenly? 0 write over the 7 Multiply 0∙8 Subtract and write remainder as a fraction.

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**The divisor and quotient are only FACTORS if the remainder is Zero.**

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**Examples with variables**

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Examples If the divisor has more than one term, always use the term with the highest degree. A remainder occurs when the degree of the dividend is less than the degree of the divisor

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Example:

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**Try These Examples Divide using long division.**

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**Long division of polynomials is tedious!**

Lets learn a simplified process! This process is called Synthetic Division p. 316 It may look complicated, but watch a few examples and you will get the hang of it.

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**Use synthetic division to divide 3x3-4x2+2x-1 by x+1**

Reverse the sign of the constant term in the divisor. Write the coefficients of the polynomial in standard form (Remember to include zeros) Translation: Instead of write Bring down the first coefficient Multiply the first coefficient by the new divisor. Add. Repeat step 3 until the end. The last number is the remainder. NOW write the polynomial. To write the answer use one less degree than the original polynomial.

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**Example: Use synthetic division to divide**

x3+4x2+x-6 by x+1 x3-2x2-5x+6 by x+2

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Remainder Theorem If a polynomial is being divided by (x-a) then the remainder is P(a). Example: Use the remainder theorem to find P(-4) for P(x)=x3-5x2+4x+12 DO NOT change the number P(a) to -a

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Try This Problem Use synthetic division to find P(-1) for P(x)=4x4+6x3-5x2-60

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Homework Practice 6.3 Evens

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