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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

-

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)