Synthetic Division 29 October 2010. Operations on Polynomials Recap – We know how to: Add Subtract...
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Transcript of Synthetic Division 29 October 2010. Operations on Polynomials Recap – We know how to: Add Subtract...
Synthetic Division
29 October 2010
Operations on Polynomials
Recap – We know how to: Add Subtract Multiply
What about division?
)2()11183( 24 xxxx
Dividing Polynomials
Like long division We have a short cut!
Synthetic Division!!!
Dividing Polynomials
Synthetic Division Only works when we divide by 1st degree (linear)
polynomials
)2()11183( 24 xxxx
My degree can’t be larger than 1!
Synthetic Division
)24()1152( 24 xxxx
)2()11183( 24 xxxx
Your Turn
On the “Synthetic Division” handout, complete problems 1 – 5. You will: Decide if it’s possible to use synthetic division to
divide the two polynomials
Division Vocab Review
Dividend Divisor
2)3()65( 2 xxxx
Quotient
Preparing for Synthetic Division
Can only be used when the divisor is in the form
x – c
If the divisor isn’t in the form x – c, then you need to convert the expression to include subtraction.
Preparing for Synthetic Division, cont.
5x 11x)11(11 xx
Preparing for Synthetic Division, cont.
Polynomials need to be written in expanded, standard polynomial form. Translation: If you’re missing terms, then you
need to write them out as 0 times (*) the appropriate term.
Preparing for Synthetic Division, cont.
xxx 273 35
xxx 273 35
020703 2345 xxxxx
Your Turn
On “Synthetic Division” handout, write the dividend in expanded standard polynomial form for problems 6 – 10.
Write the divisor in the form x – c.
))2(()0208(
)2()28(23
3
xxxx
xxx
*Synthetic Division Steps
Example Problem:
)2()11183( 24 xxxx
Prep Step
Divisor x – c? x – 2
Dividend in Expanded Standard Polynomial Form? 3x4 – 8x2 – 11x + 1 3x4 + – 8x2 – 11x + 1 3x4 + 0x3 – 8x2 – 11x + 1
Step 1
2
Write the constant value of the divisor (c) here.
Step 2
2
Write all the coefficients of the expanded dividend here.
3 0 -8 -11 1
Step 3
2
“Drop” the 1st coefficient underneath the line.
3 0 -8 -11 1
3
Step 4
2
Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.
3 0 -8 -11 1
6
3
Step 5
2
Add together the numbers in that column and write their sum underneath the line.
3 0 -8 -11 1
6
3 6
Step 6
2
Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.
3 0 -8 -11 1
6 12
3 6
Step 7
2
Repeat steps 5 and 6 until a number appears in the box underneath the last column.
3 0 -8 -11 1
6 12 8 -6
3 6 4 -3 -5
Step 8 – Naming the Quotient
2
In the last row are the coefficients of the quotient in decreasing order. The quotient is one degree less than the dividend.
3 0 -8 -11 1
6 12 8 -6
3 6 4 -3 -5
Step 8 – Naming the Quotient
3 6 4 -3 -5
The number in the box is the remainder.
)2()11183( 24 xxxx3x3 + 6x2 + 4x – 3 Remainder -5
Your Turn
On the “Synthetic Division” handout, solve for the quotient of problems 11 – 14 using synthetic division.
You may work with your partner.