Question

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction , multiplication and non – negative integer exponentiation of variables. A polynomial of degree one, two and three are called linear, quadratic and cubic polynomial respectively. Let p (x) be any polynomials of degree greater than or equal to one and let a be any real number. If p (x) is divided by the linear polynomial x – a, then the remainder is p (a).

Answer the following questions:


(a) Find the remainder when x 4 +x 3 – 2x 2 + x + 1is divided by x – 1.

(b) What is the degree of a cubic polynomial?

(c) Find the remainder obtained on dividing p (x) = x 3 + 1 by x + 1

(d) Check whether the polynomial q (t) = 4t3 + 4t2 – t – 1is a multiple of 2t +1 .

(e) Find the remainder when x 3 – ax 2 +6 x + a is divided by x – a.


Please Answer This Fast ​

Answer 1

Answer:

[tex]x3+x213x25 =x3+13x2

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer coefficients of variables with integers exponents.

Options C is not polynomials as it contains fraction as an exponent.

B as dividing is not allowed.

A satisfies the condition hence it is a polynomial.