Polynomials Test

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Polynomials Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a constant polynomial?

A
$$p(x) = \dfrac{15}{2}$$

B
$$p(x) = x$$

C
$$p(x) = x^2$$

D
$$p(x) = x^3$$

Solution

$$\textbf{Step-1: Apply the concept of polynomial.}$$

$$\text{We know that, a constant polynomial is a polynomial}$$
$$\text{that has only constant term and no variables.}$$

$$\text{Since,}$$ $$p(x)=\dfrac { 15 }{ 2 },$$ $$\text{is a polynomial with constant term}$$ $$\dfrac { 15 }{ 2 }$$
$$ \text{having no variable, it is a constant polynomial.}$$

$$\text{So,}$$ $$p(x)=\dfrac { 15 }{ 2 },$$ $$\text{is a constant polynomial.}$$

$$\textbf{Hence, correct option is A}$$
Question 2
1 / -0

Which of the following is a constant polynomial?

A
$$p(x) = 7 + 3x$$

B
$$p(x) = 7 $$

C
$$p(x) = 7x + 7$$

D
$$p(x) = 4x + 3$$

Solution

Since $$p(x)=7$$ is a polynomial with constant term $$7$$ and there is no variable in it.

Hence, $$p(x)=7$$ is a constant polynomial.
Question 3
1 / -0

Which of the following is a constant polynomial?

A
$$p(x) = x^1$$

B
$$p(x) = x^0$$

C
$$p(x) = x^2$$

D
$$p(x) = x^3$$

Solution

We know that if the power of any variable is zero then the answer is always $$1$$.

Therefore, $$p(x)=x^0$$ or $$p(x)=1$$ is a polynomial with constant term $$1$$ and there is no variable in it.

Hence, $$p(x)=x^0$$ is a constant polynomial.
Question 4
1 / -0

Which of the following is a constant polynomial?

A
$$p(x) = \sqrt{81}$$

B
$$p(x) = 8 + x$$

C
$$p(x) = 8x + 1$$

D
$$p(x) = x$$

Solution

Since $$p(x)=\sqrt { 81 }$$ is a polynomial with constant term $$\sqrt { 81 }$$ and there is no variable in it.

Hence, $$p(x)=\sqrt { 81 }$$ is a constant polynomial.
Question 5
1 / -0

$$p(x) = c$$, where $$c$$ is a real number. $$p(x)$$ is a

A
linear polynomial

B
quadratic polynomial

C
cubic polynomial

D
constant polynomial

Solution

Since $$p(x)=c$$ is a polynomial with only constant term $$c$$ and no variable term present in the it.
Hence, $$p(x)$$ is a constant polynomial.
Question 6
1 / -0

$$p(x) = 6x^2 - 2x^6 $$ is a polynomial in $$x$$ of degree

A
$$6$$

B
$$3$$

C
$$1$$

D
none of these

Solution

$$p(x) = 6x^2 - 2x^6$$.
Here, the highest degree of the variable $$x$$ is $$6$$.
$$\therefore p(x)$$ is a polynomial of degree $$6$$
Question 7
1 / -0

What is the degree of the polynomial $$p(x) = 5x^3 - 8x^2 + 4x?$$

A
$$3$$

B
$$2$$

C
$$1$$

D
$$0$$

Solution

The polynomial $$ax^3+ bx^2+cx+d=0$$ is in standard form.
On comparing $$5x^3-8x^2+4x$$ with the standard form, the power of the first term is $$3$$, the power of the second term is $$2$$ and the power of the third term is $$1$$. Since the polynomial has the largest exponent, that is $$3$$ which is the degree of the polynomial.

Hence, the degree of the polynomial is $$3$$
Question 8
1 / -0

Which of the following is NOT a linear polynomial?

A
$$p(x) = 2x + 3$$

B
$$p(x) = 4x^0 + 3$$

C
$$p(x) = 4x + 3$$

D
$$p(x) = 2 + 3x$$

Solution

$$\textbf{Step1: Check Every Option to find whether it is Linear Polynomial or Not}$$
$$\text{The General Form of linear polynomial is p(x)=ax+b}$$
$$\text{where x is a Variable and b is a Constant}$$
$$\text{The first term of this polynomial has power 1 and Therefore, the degree of the polynomial is 1.}$$
$$\text{By Verifying every option,we can say that-}$$
$$\text{Only Polynomial given in option B- $p(x)=4x^0+3$ has degree 0}$$.

$$\textbf{Hence, the polynomial p(x)=$\boldsymbol{4x^0+3}$ is not a Linear Polynomial.}$$
Question 9
1 / -0

What is the degree of the polynomial $$p(x) = 8x^8 + 9x^9 + 10x^0$$?

A
$$8$$

B
$$9$$

C
$$10$$

D
$$0$$

Solution

After writing the $$9x^9+8x^8+10x^0$$ we can see that the power of the first term is $$9$$, the power of the second term is $$8$$ and the power of the third term is $$0$$. Since the polynomial has the largest exponent, that is $$9$$ which is the degree of the polynomial.

Hence, the degree of the polynomial is $$9$$.
Question 10
1 / -0

Which of the following is not a constant polynomial?

A
$$p(x) = 3^3$$

B
$$p(x) = 2^3$$

C
$$p(x) = x^3$$

D
$$p(x) = 4^3$$

Solution

$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{We know that cubic power of a constant is also a constant.}$$
$$\text{Therefore,}$$ $$p(x)=x^3$$ $$\text{is a polynomial with variable}$$ $$x$$ $$\text{and there is no constant term in it.}$$
$$\text{So,}$$ $$p(x)=x^3$$ $$\text{is not a constant polynomial.}$$
$$\textbf{Hence, correct option is C}$$

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Polynomials Test - 38

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Polynomials Test - 38

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Question 1

$$p(x) = \dfrac{15}{2}$$

$$p(x) = x$$

$$p(x) = x^2$$

$$p(x) = x^3$$

Solution

Question 2

$$p(x) = 7 + 3x$$

$$p(x) = 7 $$

$$p(x) = 7x + 7$$

$$p(x) = 4x + 3$$

Solution

Question 3

$$p(x) = x^1$$

$$p(x) = x^0$$

$$p(x) = x^2$$

$$p(x) = x^3$$

Solution

Question 4

$$p(x) = \sqrt{81}$$

$$p(x) = 8 + x$$

$$p(x) = 8x + 1$$

$$p(x) = x$$

Solution

Question 5

linear polynomial

quadratic polynomial

cubic polynomial

constant polynomial

Solution

Question 6

$$6$$

$$3$$

$$1$$

none of these

Solution

Question 7

$$3$$

$$2$$

$$1$$

$$0$$

Solution

Question 8

$$p(x) = 2x + 3$$

$$p(x) = 4x^0 + 3$$

$$p(x) = 4x + 3$$

$$p(x) = 2 + 3x$$

Solution

Question 9

$$8$$

$$9$$

$$10$$

$$0$$

Solution

Question 10

$$p(x) = 3^3$$

$$p(x) = 2^3$$

$$p(x) = x^3$$

$$p(x) = 4^3$$

Solution

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