Question

write three more polynomials and create three questions for each of the them​

Answer 1

Answer:

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Swarup1998 Genius

Polynomials

Definition. An expression of the form

\quad a_{0}x^{n}+a_{1}x^{n-1}+...+a_{n-1}x+a_{n},

where a_{0},\:a_{1},\:...,\:a_{n} are given numbers (real or complex), n is a non-negative integers and x is a variable, is called a polynomial in x or a rational integral function of x.

Writing three polynomials and questions related to them:

1. Find the remainder when 4x^{5}+3x^{3}+6x^{2}+5 is divided by 2x+1. Here 4x^{5}+3x^{3}+6x^{2}+5 is a polynomial in x.

2. Expand f(x)=x^{4}-4x^{3}+3x^{2}+3x+7 as a polynomial in x-1. Here f(x)=x^{4}-4x^{3}+3x^{2}+3x+7 is a polynomial in x.

3. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x^{2}-3x+7

(ii) y^{2}+\sqrt{2}

(iii) 3\sqrt{t}+t\sqrt{2}

(iv) y+\frac{2}{y}

(v) x^{10}+y^{3}+t^{50}

Answer 2

Answer:

Three polynomials -

X^2 - 49 {Quadratic P(x) }

X^3 - X^2 + X + 4 {Cubic P(x)}

X^4 + 25X^2 + 17x -216 {Bi Quadratic P(x)}

Question for them

Find all the roots of P(x) {the first polynomial}

Divide P(x) {the second polynomial} by X^2 -2

Find all the zeros of the P(x) {the third polynomial} if two zeros are -5,7