I’ve already explained some of the basic and elementary topics related to polynomials (for the topic click here) and here in this space one more topic is remaining i.e. long Division.

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Long Division of polynomials

If a polynomial p(x) is divided by another polynomial say g (x) and

**quotient**as q(x) and**remainder**as r(x) then these set of polynomials can be represented as Euclid’s Division Algorithm i.e.### • p(x) = q(x) × g(x) + r(x)

According to our topic we are to divide p(x) by g(x) so,

**• p(x) / g(x) = q(x)**if remainder becomes 0.

if remainder doesn’t becomes 0 then above relationship can be rearranged as

**• [p(x) – r(x) ] / g(x) = q(x)**

for practice let’s take an example:

in this above image an example is taken in which p(x) = x² + 7x +12 is divided by

g(x)= x+3 and resultant quotient is q(x)= x+4.

### Steps for long Division method –

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**make the same term**– take a look at the first term of both dividend and Divisor, to male the same term of g(x) as p(x)’s first term we should choose a suitable term. In above example x is chosen so that when it is multiplied by x ( g(x)’s first term) it will give us x² (p(x)’s first term).

__Do not forget__– yes…!!! of course this step can’t be missed out, as most of the students makes mistake by forgetting other terms of g(x) which should also be multiplied and resultant should placed under p(x)’s other respective terms.In above example x of quotient is multiplied by 3 and 3x is placed under 7x because of like terms.

__Subtract and proceed__– now after multiplying all the terms move onto subtraction as normal subtraction.In above example 4x + 12 is remaining after subtracting, after doing this, proceed the same process until we get either remainder 0 or degree of remainder less than that of g(x).

*– take a look at the first term of both dividend and Divisor, to male the same term of g(x) as p(x)’s first term we should choose a suitable term. In above example x is chosen so that when it is multiplied by x ( g(x)’s first term) it will give us x² (p(x)’s first term).***make the same term****– yes…!!! of course this step can’t be missed out, as most of the students makes mistake by forgetting other terms of g(x) which should also be multiplied and resultant should placed under p(x)’s other respective terms.In above example x of quotient is multiplied by 3 and 3x is placed under 7x because of like terms.**__Do not forget__**– now after multiplying all the terms move onto subtraction as normal subtraction.In above example 4x + 12 is remaining after subtracting, after doing this, proceed the same process until we get either remainder 0 or degree of remainder less than that of g(x).**__Subtract and proceed__
So these are three simple easy steps which I found to be

**remarkable**for your solutions of same problems.
Now check out an another example-

If still you are finding difficulties feel free to comment under the post in comment box.

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