Polynomials Test

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Polynomials Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following polynomial defines constant polynomials?

A
$$p(x) = ax^3 + bx^2 + cx + d$$

B
$$p(x) = ax^2 + bx + c$$

C
$$p(x) = c$$

D
$$p(x) = ax + b$$

Solution

Since a polynomial $$p(x)=c$$ is a constant polynomial with constant term $$c$$,

A polynomial $$ax^2+bx+c$$ is a quadratic polynomial with variables $$x,y$$ and constant $$c$$ and

A polynomial $$ax+b$$ is a linear polynomial with variable $$x$$ and constant $$b$$

Hence, $$p(x)=c$$ is a constant polynomial.
Question 2
1 / -0

Which of the following is NOT a constant polynomial?

A
$$p(z) = z^o$$

B
$$p(y) = y^o$$

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

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

Solution

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

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

$$\text{For example,}$$ $$x^0=1$$ $$\text{which is a constant polynomial.}$$ $$\text{As there is no variable in it.}$$

$$\text{Since}$$ $$p(x)=x^1$$ $$\text{or}$$ $$p(x)=x$$ $$\text{is a polynomial with variable}$$ $$x$$ $$\text{and there is no constant term in it.}$$

$$\text{So,}$$ $$p(x)=x^1$$ $$\text{is not a constant polynomial.}$$

$$\textbf{Hence, correct option is D}$$
Question 3
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

$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{We know that cubic power of a constant is also a constant.}$$
$$\text{Therefore,}$$ $$p(x)=x^3$$ $$\text{is a polynomial with variable}$$ $$x$$ $$\text{and there is no constant term in it.}$$
$$\text{So,}$$ $$p(x)=x^3$$ $$\text{is not a constant polynomial.}$$
$$\textbf{Hence, correct option is C}$$
Question 4
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 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

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 7
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 8
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 9
1 / -0

Which of the following is NOT a constant polynomial?

A
$$p(y) = y^o$$

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

C
$$p(y) = \dfrac{y}{y}$$

D
$$p(x) = yx$$

Solution

We know that if the power of any variable is zero then the answer is always $$1$$. For example, $$x^0=1$$ which is a constant.

Since $$p(x)=yx$$ is a polynomial with variables $$x,y$$ and there is no constant term in it.

Hence, $$p(x)=yx$$ is not a constant polynomial.
Question 10
1 / -0

$$p(5) = 5$$ then, which polynomial from the following, it corresponds to?

A
$$p(x) = x^2 - 5x + 5$$

B
$$p(x) = x^2 - 5x$$

C
$$p(x) = x^2 - x + 5$$

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

Solution

Let $$p(x)=x^2-5x+5$$ and substitute $$x=5$$ as shown below:

$$p(5)=(5)^{ 2 }-\left( 5\times 5 \right) +5=25-25+5=5$$

Hence, $$p(x)=x^2-5x+5$$.

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 37

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Polynomials Test - 37

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SHARING IS CARING

Question 1

$$p(x) = ax^3 + bx^2 + cx + d$$

$$p(x) = ax^2 + bx + c$$

$$p(x) = c$$

$$p(x) = ax + b$$

Solution

Question 2

$$p(z) = z^o$$

$$p(y) = y^o$$

$$p(x) = x^o$$

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

Solution

Question 3

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

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

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

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

Solution

Question 4

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

$$p(x) = x$$

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

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

Solution

Question 5

linear polynomial

quadratic polynomial

cubic polynomial

constant polynomial

Solution

Question 6

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

$$p(x) = 7 $$

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

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

Solution

Question 7

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

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

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

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

Solution

Question 8

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

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

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

$$p(x) = x$$

Solution

Question 9

$$p(y) = y^o$$

$$p(x) = x^o$$

$$p(y) = \dfrac{y}{y}$$

$$p(x) = yx$$

Solution

Question 10

$$p(x) = x^2 - 5x + 5$$

$$p(x) = x^2 - 5x$$

$$p(x) = x^2 - x + 5$$

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

Solution

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