Question

What is remainder theorem? How should we do the answer if they ask us to write the answer using remainder theorem?
Explain the answer with an example

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Answer 1

Answer:

The Remainder Theorem begins with a polynomial say p(x), where “p(x)” is some polynomial p whose variable is x. Then as per theorem, dividing that polynomial p(x) by some linear factor x – a, where a is just some number. Here go through a long polynomial division, which results in some polynomial q(x) (the variable “q” stands for “the quotient polynomial”) and a polynomial remainder is r(x). It can be expressed as:

p(x)/x-a = q(x) + r(x)

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Answer 2

first observe, this attachment

f(x) should be read as "f of x"

here, there is an expression given in f(x)

there can be any alphabets used in the place of 'f'

now, they asked us to divide f(x) by x-2

f(x) will be called as 1st expression and

x-2 will be called as 2nd expression

the questions of remainder theorem will be like,

• divide f(x) by x-2
• divide f(x) by x+3
• and so on...

here in this attachment, they question was like,

divide f(x) by x-2

if the question was asked like this,

The first step is we have to find the value of x

so, now you will have a question..

"how to find the value of x?"

it is very easy.

To find the value of x..

first we have to see the 2nd expression.

We can find the x by using transposing method,

always, we have to take that the value of the 2nd expression as zero.

so here, in this 2nd expression

x-2 = 0

now by transposing 2 to the right side we will have,

x = 0+2

so, x = 2

now, we have found the value of x.

then, the second step is substitution.

we have to substitute the value of x in the first expression f(x)

so here in the question,

they have given.. f(x) = x^3 + x^2 + x + 6

so, we have to put 2 in the place of x

now, by putting 2 in the place of x

we will get, 2^3 + 2^2 + 2 + 6

= 8 + 4 + 2 + 6

= 20

now, we have found the remainder by using substitution method.

This is called as remainder theorem.

only 2 steps and also very easy.

There is also one more method in remainder theorem which is called as long division method.

If you are clear with my concepts and want me to explain about it I will explain it also..