Download - 8.3 8.4 Dividing Polynomial
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P.O.D.
Ifr varies jointlyas s & tand
inversely as u,and r=18 when
s=2, t=3, andu=4, find s when= = =
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= = =
8.3-DividingPolynomialsDividing one
polynomial byanother polynomial
of lower or equal
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The Division Algorithm
divisor
remainderquotient
Divisor
Dividend +
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The Division Algorithm
divisor
remainderquotient
Divisor
Dividend +
e egreeof the
remaindermust beless thanthe degree
of thedivisor
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Using LongDivision
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Divide 2x4+3x3+5x-
1 by x2-2x+2
1st) Make sure
terms are indegree order
Dividend Divisor
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2nd)Set up thedivision box
503222
2342
xxxxxx
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2nd)Set up thedivision box
503222
2342
xxxxxx
Include a 0 asthe coeff. of x2.
(Do this for any
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3rd
)StartDividing!!
What termmultiplied to x2
gives 2x4
?
1503222 2342 xxxxx
22x
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3rd
)StartDividing!!
What termmultiplied to x2
gives 2x4
?
1503222 2342 xxxxx
22x
Since divisor has 3terms, 2x2 is placed
over 3rd term in
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4th
)Multiply 2x2
to everything in
divisor & placeunder
a ro riate terms
1503222 2342 xxxxx
22x
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1503222 2342 xxxxx
22x
234442 xxx +
Subtracall
xxx 54723 +
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Repeat theprocess using
th ivi n
1503222 2342 xxxxx
22x
234442 xxx +
xxx 54723 +
xxx 54723 +
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Divide:
1.
2.
223
44692
34
++
uu
uuu
22
4334
2
6
cctt
ctcctt
++
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P.O.D.
Divide:
223
44692
34
++
uu
uuu
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8.4Using Synthetic
Division
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Synthetic Division
A way of dividing
a polynomial by abinomial of theformx k, where
k is a constant
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v e x -5x3+7x2+3x+2 by x
-3 Write the
coefficients of thedividend under thedivision box (makesure you supply a 0for any missing term)
and in the divisor
237523
Bring down the
first coefficient ofthe dividend2.
2
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Repeat with 1 andrepeat process
until the end. Multiply 3 and 2and place theproduct, 6, underthe second
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237523
261
310
3033
99101
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Write your answeras:
2x3+x2+10x+33
237523
261
310
3033
99101
Note that the
leading term hasan x3 rather than
an x4Always 1less than the
highest degree ofthe dividend.
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Divide x4+5x3-9x+6byx+2Make sure you
supply themissing term 0x2
as ou would in
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HW:
Pg. 366-67 (4-28every 4th)
Pg. 370 (1-12)