chapter 6 section 3 dividing polynomials. long division vocabulary reminders
TRANSCRIPT
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Chapter 6
Section 3
Dividing Polynomials
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Long Division Vocabulary Reminders
quotient
dividenddivisor
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Remember Long DivisionRemember Long Division1. Does 8 go into 6?
• No
2. Does 8 go into 64?• Yes, write the integer on
top.
3. Multiply 8∙8• Write under the dividend
4. Subtract and Carry Down5. How many times does 8
go into 7 evenly?• 0 write over the 7
6. Multiply 0∙8 7. Subtract and write
remainder as a fraction.
6478
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The divisor and quotient are only FACTORS if the remainder is Zero.
quotient
dividenddivisor
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Examples with variables
22xx 393 yy
2164 ww 3362 xx
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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:
7621 2 xxx
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Try These ExamplesDivide using long division.
)1()783( 2 xxx
)3()146( 2 xxx
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Long division of polynomials is tedious!
Lets learn a simplified process!This process is called Synthetic Division
p. 316It 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
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
write2. Bring down the first coefficient3. Multiply the first coefficient by the new
divisor. Add.4. Repeat step 3 until the end. The last
number is the remainder.5. NOW write the polynomial.
To write the answer use one less degree than the original polynomial.
12431 2 xxxx
-1 3 -4 2 -1
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Example: Use synthetic division to divide
a) x3+4x2+x-6 by x+1
b) 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