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Strategic Plan On How To Study

POLYNOMIALS AND DIVISION ALGORITHM

I. Related Toic! 

Operation on Integers

  Addition

  Subtraction

 

Multiplication

  Division

 

Exponents

 

Binomials

II. "oncet! and Idea!A olyno#ial is an expression consisting of variables and coecients, th

involves onl the operations of addition, subtraction, multiplication, and no

negative integer exponents"A olyno#ial e$uation is an e#uation that can be $ritten in the form ax %

% c & ', $here a, b, and c are real numbers"Ter# is the part that is being added" (olnomial terms have variables $hich a

raised to $hole!number exponents" )he leading ter# of a polnomial is the term $ith the highest degree"

 )he degree of a polnomial is the highest degree of its terms" (olnomials a

also sometimes named for their degree* a second!degree polnomial, such as +x%, x%  -, or ax% % bx % c, is al

called a .#uadratic. a third!degree polnomial, such as /x0 or x0  12, is also called a .cubic.

a fourth!degree polnomial, such as x& or 1x&  0x1 % -, is sometim

called a .#uartic. a 3fth!degree polnomial, such as 1x' or x'  +x0  x % 2, is sometim

called a .#uintic. )he leading coe(cient of a polnomial is the coecient of the leading term"

)*a#le!+

(olnomials4o" of 

terms

Degre

e

5eading

 )erm

5eading

6oecie

nt

+x7  17x+ % +'x0 % 0x1  89x % - / 7th +x7 +

2x % 87 81x+  +x0 + +th 81x+ 81x0 % +x+  11x 87 + +th +x+ +

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Di,i!ion o- Polyno#ial!

 Polyno#ial long di,i!ion is an algorithm for dividing a polnomial b anoth

polnomial of the same or lo$er degree, a generalised version of the famil

arithmetic techni#ue called long division"Example*

8" 7x1

! 82x ! 87 : x ! +

1" /x0 ! 8/x1 % 82x / : 0x ! 1

Syntetic di,i!ion is a shorter procedure $hen a polnomial

to be divided b a binomial ;x r<" In this procedure $e $rite onl t

coecients")*a#le+ P/*0 1 2* 3 &* 3 4 divided b * 3 %

Ste 5+ Arrange the coecients of (;x<

in descending po$ers of x, placing=eroes >'? for the missing terms" )he

leading coecient of (;x< becomes the

3rst entr of the third ro$"

Ste %+ (lace the value of r in the upper

left corner" In this example, x r & x % 1

& x ;!1<, so r & 1"

Ste 2+ )he 3rst number in the second

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ro$ ;!/< is the product of r  ;!1< and the

number in the third ro$ ;0< of the

preceding column, the second number

in the third ro$ ;!1< is the sum of the

t$o numbers ;+ and !/< above it"Ste &+ @epeat the procedure described

in step 0 until the last number in the

third ro$ is obtained"

Ste 2+ rite the #uotient ;x<" 4ote

that the degree of ;x< is one less than

the degree of (;x<" )he entries in the

third ro$ give the coecients of ;x<

and the remainder @"

)*a#le!+

5. *2 3 6*% 3 %* 7 &8 9 * 7 %

%. *2 3 2' 3 :*% 3 52* 9 * ; '

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8st (olnomial 1nd (olnomial uotient@emainde

r

x0 % +x1  x 17 x % 7 x1  x % + +7

1x+ % 7x0 % 0x1 % 9x %81 1x % 0 x0 % x1% + '

III. Su##ary< "onclu!ion and In!igt!A polnomial is an expression that consists of variables and coecients" )e

have variables $hich are raised to $hole!number exponents and it is the part that

being added" )he degree is the highest degree of its terms and the leading term

the term $ith the highest degree" 5ong division is dividing a polnomial b anoth

polnomial of the same or lo$er degree $hile snthetic division is the shorter $

of dividing polnomials"I therefore conclude that using snthetic division in dividing polnomials $e

easier than the long method but in order to maCe sure that the resulting ans$er

correct, $e should rechecC it or tr the other $a of dividing polnomial ;lon

division<" I therefore conclude also that using or appling the concepts from our pa

lesson liCe exponent, integers and so on can help us to divide polnomials"nfortunatel, this is m 3rst strategic plan in fourth #uarter but this strateg

plan helps me a lot" I learn more about division of polnomial in this strategic plan

$ish I can pass the other test so that I $ill not able to maCe another strategic pla

M lesson in this test is dont be careless, solve the problems carefull and $rite t

ans$er in the test paper carefull" Even though our solution is correct and th

ans$er in the scratch paper is correct but $hen ou $rote the 3nal ans$er in t

test paper there is something $rong and I reali=e that the ans$er I $rote $

incorrect due to carelessness" And the greatest lesson Ive learned in the test $

=)RO IS NOT POLYNOMIAL and >4ASA F5I A4G (AGSISISI?"

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