Question

answer this..
no spam..​

Answer 1

Ques:1

Remainder Theorem:-

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a). So basically, x -a is the divisor of P(x) if and only if P(a) = 0. It is applied to factorize polynomials of each degree in an elegant manner.

For example:-

if f(a) = a3-12a2-42 is divided by (a-3) then the quotient will be a2-9a-27 and

the remainder is -123.

if we put, a-3 = 0

then a = 3

Hence, f(a) = f(3) = -123

Thus, it satisfies the remainder theorem.

Factor Theorem:-

According to factor theorem, if f(x) is

a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x),

if f(a)=0.

Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This proves the converse of the theorem. Let us see the proof of this theorem along with examples.

Factor theorem is commonly used for factoring a polynomial and finding the roots of the polynomial. It is a special

case of a polynomial remainder theorem.

As discussed in the introduction, a polynomial f(x) has a factor (x-a), if and

only if, f(a) = 0. It is one of the methods to do the factorisation of a polynomial.

Ques:3

• Identity I: (a + b)2 = a2 + 2ab + b2

• Identity III: a2 – b2= (a + b)(a – b)

• Identity IV: (x + a)(x + b) = x2 + (a + b)

x + ab.

• Identity V: (a + b + c)2 = a2 + b2 + c2 +

2ab + 2bc + 2ca.

Refer to the attachment ...

Answer 2

Answer:

Sry mai tho back bencher hu.

Vidya ko kavie friend nhi bana sktha.. Hehe