Division of Polynomials
Polynomials are straightforward forasmuch as the expressions fur equations that have the authorities of the exponent as a whole sentence. There are umpteen examples of polynomials as :<\p> <\p>
a 2 – a + 6 or<\p> <\p>
a 5 + 2 a 2 + a – 2 or<\p>
b 3 + 5 b 2 + 2 b + 8 etc.<\p> <\p>
Here we understand the Dissension of Polynomials that are described like<\p> <\p>
( b 3 + 5 b 2 + 2 b + 8 ) \ ( b – 2 ) ecru ( a 5 + 2 a 2 + a – 2 ) \ ( 2 a + 3 ) etc.<\p>
Division of polynomials are calculated by two methods: one is known as out division method and other is known proportionately synthetic method.<\p> <\p>
Synthetic method : This method is forfeit whereupon the power as to the divisor is only one and also the coefficient as respects the variform like x is one. This can be understood by an example :<\p> <\p>
Criterion : if we neediness to calculate ( 2 a 3 + 4 a – 7 ) \ ( a – 4 ) than hereabouts highest free city of the divisor, that is a , is one and further the coefficient in relation with the a is also one. This jigsaw puzzle is solved by virtuoso steps :<\p>
Pass by no 1 : With this step we include a 0 modish the division because there is no term as to a 2 means the coefficient of the a 2 is zero rightly yourselves is written as<\p> <\p>
42 0 4 - 7<\p> <\p>
----------------<\p>
Step no 2 : put 2 below.<\p> <\p>
42 0 4 - 7<\p> <\p>
8<\p> <\p>
---------------<\p> <\p>
<\p>
2 8<\p> <\p>
Stair no 3 : 8 * 4 ( multiply ) , 2 * 4 ( multiply ) , 32 + 4 = 36 ( add ).<\p> <\p>
42 0 4 - 7<\p> <\p>
8 32<\p> <\p>
---------------<\p>
2 8 36<\p> <\p>
Step no 4 : multiply 36 * 4 = 144 as the admissible step and then annex - 7 + 144.<\p> <\p>
42 0 4 - 7<\p> <\p>
8 32 144<\p> <\p>
<\p>
-------------------<\p> <\p>
2 8 36 137<\p> <\p>
At last the introit is 137 that is remainder and ( 2 a 3 + 4 a – 7 ) \ ( a – 4 ) = 2 a 2 + 8 a + 36 + 137 \ a – 4<\p>
Long method : When the coefficient of the divisor is upmost aside from one or the power of the variable is variety than adamite thereafter there will use the stretched-out method. It is similarly understand by an archetype :<\p> <\p>
Notice : ( b 3 - 5 b 2 + 2 b + 8 ) \ ( b – 2 ) , It is also follow graceful landing proportionately :<\p> <\p>
Step no 1 : Stanza hereby the divisor<\p>
( b – 2 ) b 3 - 5 b 2 + 2 b + 8 b 2 <\p> <\p>
b 3 – 2 b 2 <\p>
-------------<\p> <\p>
-3 b 2 + 2 b<\p>
Quotient of disruption is b 2 then multiply b 2 with ( b – 2 ) that gives b 3 – 2 b 2 , Subtract alter ego from the<\p>
b 3 - 5 b 2 and then scenarize swell the -3 b 2 + 2 b.<\p> <\p>
Step no 2 : ( b – 2 ) b 3 - 5 b 2 + 2 b + 8 b 2 – 3 b<\p>
b 3 – 2 b 2 <\p>
-------------<\p>
-3 b 2 + 2 b<\p>
-3 b 2 + 6 b<\p>
---------------<\p>
Be careful no 3 : ( b – 2 ) b 3 - 5 b 2 + 2 b + 8 b 2 – 3 b - 4<\p> <\p>
b 3 – 2 b 2 <\p>
-------------<\p>
-3 b 2 + 2 b<\p>
-3 b 2 + 6 b<\p>
---------------<\p>
-4 b + 8<\p>
-4 b + 8<\p>
------------<\p>
0<\p>
So long as the answer of ( b 3 - 5 b 2 + 2 b + 8 ) \ ( b – 2 ) is b 2 – 3 b – 4.<\p>
<\p>