Polynomial and Its General Form

Q.

Question 1
Which one of the following is a polynomial?

A) $\frac{x^2}{2}-\frac{2}{x^2}$
B) $\sqrt{2x}-1$
C) $x^2+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}$
D) $\frac{x-1}{x+1}$

Q.

The number of polynomials having zeroes as$-2$ and$5$ is

1. $1$

2. $2$

3. $3$

4. $morethan3$

Q.

What is degree of polynomial root3

Q. Why is the degree of a zero polynomial not defined?

Q.

The numerical factor of a term is known as

1. Expression

2. Coefficient

3. Variable

4. Equation

Q.

Give an example of a trinomial of degree $7.$

Q. Question 2
The polynomial $p\left(x\right)=x^4–2x^3+3x^2–ax+3a–7$ when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

Q. Question 3(iv)
Express the number appearing in the following statements in standard form:
Size of a plant is 0.00001275 m.

Q.

Which table shows exponential decay?

1. 

2. 

3. 

4. 

Q. Question 4
Write the degree of each of the following polynomials:
(i) $5x^3+4x^2+7x$
(ii) $4-y^2$
(iii) $5t-\sqrt{7}$
(iv) 3

Q.

Question 115(vii)

Express the following in standard form:
Express 2 yr in seconds.

Q.

Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?

Q.

What is the degree of the 0 polynomial

Q.

Question 141

One fermi is equal to ${10}^{-15}$ metre. The radius of a proton is 1.3 fermi. Write the radius of a proton (in metres) in standard form.

Q.

Which of the following are like terms to $9p{q}^2$?

1. $8ab$
2. $5bc$

3. $5q^{2}p$

4. $12p{q}^2$

Q. Solve:-
$x^3-3x^2-9x-5$

Q. Coefficient of ${}^{\prime }{b}^{\prime }$ in the expression $4b^2$ is ___.

1. 4
2. $b$
3. 2
4. $4b$

Q.

Degree of the polynomial 0x²

Q.

Give an example of a monomial of degree$11$.

Q. If $a+b+c=0$, then the value of $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}$ is

1. 1
2. \N
3. -1
4. 3

Q. It is given that the polynomial $p\left(x\right)=x^3-9x^2+26x+24$ has zeroes that are integers. Which of the following is not a zero of the polynomial.

1. 5
2. 2
3. 3
4. 4

Q.

Identify terms that contain $x$ and give the coefficient of $x$.

$y^{2}x+y$

Q. What is the coefficient of -x in $-42x{y}^3{z}^2$?

1. 42
2. -42$y^3$$z^2$
3. -42
4. 42$y^3$$z^2$

Q.

What is a polynomial?

Q.

Q.

Write the degree of the following expressions:

$2x^5{y}^4+x^5{y}^7-x^{4}y$

Q. If $x=\frac{5-\sqrt{21}}{2}$ , then
$(x^3+\frac{1}{x^3})-5(x^2+\frac{1}{x^2})+(x+\frac{1}{x})=$

1. 1
2. 2
3. -1
4. 0

Q. State whether the given algebraic expressions are polynomials ? Justify.
$2m^{-2}+7m-5$

Q.

Which of the following polynomials does not has a degree $3$ ?

1. $2x^3–5x^2+ax+b=0$

2. $6x^3–11x^2+kx=20$

3. $3x+8=4$

4. $\sqrt[3]{x^2}=x$

Q. Simplify:-
$x^3+13x^2+32x+20$