Question

what is meant by remainder theorem

Answer 1

Let p(x) be any polynomial of degree greater than or equal to one let A be any real number of p(x) is divided by the linear polynomial x-a,then the remainder is p(a).

Answer 2

HEY MATE!  

HERE'S YOUR ANSWER!

 " Remainder theorem "  

Consider two numbers 15 and 6.

 You know that when we divide 15 by 6, we get quotient to and remainder 3.  

And, we write a formula for checking our answer , i.e,  

Divided = divisor × quotient + Remainder  

So, it will be ,  

​15 = (6×2)+3  

15 = (6×2)+3  

We observe that the remainder 3 is less than the devisor 6.  

Similarly, if we divide 2 by 6 we get,   12 = (6×2)+0  What is the remainder here?  

here the remainder is zero and we say that 6 is a factor of 12 or 12 is a multiple of 6.  

Now the question is : can we divide 1 polynomial by another? To start with let's try and do this when a divisor is a monomial.

So let us devide the polynomial 2x³+x²+x by the monomial x.  

So, (2x³+x²+x) ÷ x  

= $\frac{2x^3}{x} + \frac{x^2}{x} + \frac{x}{x} \\ \\ = </p> <p>2x^2 + x + 1$

 in fact, you may have noticed that x is common to each term of this polynomial.

so we can write,  x(2x²+x+1).  

We say that x and 2x²+x+1 are factors of 2x³+x²+x, and 2x³+x²+x is a multiple of x as well as a multiple of 2x²+x+1 .  

Hope you understood!