Polynomials Test

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Polynomials Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

The variable in the quadratic polynomial $$t^2+4t+5$$ is

A
$$1$$

B
$$4$$

C
$$t$$

D
$$5$$

Solution

Since in a standard quadratic polynomial $$x^2+x+a$$, $$x$$ is a variable and $$a$$ is a constant term, therefore, in the given polynomial $$t^2+4t+5$$ we have variable $$t$$ and $$5$$ is a constant term.
Hence, the variable of the given quadratic polynomial is $$t$$.
Question 2
1 / -0

$$p(a) = 3a^2 + 4a - 4$$ is a polynomial in $$a$$ of degree

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

Solution

The polynomial $$ax^2+bx+c$$ is in standard form.On comparing $$3a^2+4a-4$$ with the standard polynomial we see, the power of the first term is $$2$$. Since the polynomial has the largest exponent, that is $$2$$ which is the degree of the polynomial.

Hence, the degree of the polynomial is $$2$$.
Question 3
1 / -0

The _________ power of the variable in a polynomial is called its degree.

A
highest

B
lowest

C
negative

D
none of these

Solution

The polynomial $$x^2+x+a$$ is in the standard form.

The power is simply the number in the exponent.
In the polynomial, $$x^2+x+a$$, the power of the first term is $$2$$. Since the polynomial has the largest exponent of the variable $$x$$ as $$2$$, it is the degree of the polynomial.

Hence, the highest power of the variable in a polynomial is called its degree.
Question 4
1 / -0

Identify the degree of the given equation: $$\displaystyle { x }^{ 2 }+3x-5={ x }^{ 2 }+9x-23$$

A
Zero

B
One

C
Two

D
Three

Solution

$$x^2+3x-5=x^2+9x-23$$
We need to bring the given equation to it standard form.
$$\therefore -5+23=9x-3x$$ .....Transpose
$$\therefore 18 = 6x$$
$$\therefore x=3$$

Here, the highest power of variable $$x$$ is $$1$$.
Hence, the degree of the given equation is $$1$$.
Question 5
1 / -0

The highest power of the variable in a polynomial is called its _______.

A
degree

B
constant

C
zero

D
co-efficient

Solution

The polynomial $$x^2+x+a$$ is in the standard form.

The power is simply number in the exponent. In the polynomial, $$x^2+x+a$$, the power of the first term is $$2$$. Since the polynomial has the largest exponent that is $$2$$, which is the degree of the polynomial.

Hence, the highest power of the variable in a polynomial is called its degree.
Question 6
1 / -0

$$5x + 3$$ is a polynomial in $$x$$ of degree

A
$$2$$

B
$$1$$

C
$$3$$

D
$$5$$

Solution

The given polynomial is $$5x+3$$

The power of $$x$$ in the first term is $$1$$,and the power of $$x$$ in the second term is $$0$$
Since in the polynomial the largest exponent of $$x$$ is $$1$$, it is the degree of the polynomial.

Hence, the degree of the polynomial is $$1$$
Question 7
1 / -0

Which of the following is NOT a constant polynomial?

A
$$p(x) = 15$$

B
$$p(x) = 1$$

C
$$p(x) = x$$

D
$$p(x) = 20$$

Solution

$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{Since}$$ $$p(x)=x$$ $$\text{is a polynomial with variable}$$ $$x$$ $$\text{and there is no constant term in it.}$$
$$\text{In the other given options, we can see that the polynomials have}$$
$$\text{constant terms, none of them has any variable term.}$$
$$\text{So,}$$ $$p(x)=x$$ $$\text{is not a constant polynomial.}$$
$$\textbf{Hence, correct option is C}$$
Question 8
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 9
1 / -0

$$p(y) = 5y^3 - 2y^2 + y + 10$$ is a polynomial in $$y$$ of degree

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

in $$5y^3-2y^2+y+10$$ we see 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 10
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

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

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

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

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

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

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

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Polynomials Test - 37

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Polynomials Test - 37

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Question 1

$$1$$

$$4$$

$$t$$

$$5$$

Solution

Question 2

$$4$$

$$3$$

$$2$$

$$1$$

Solution

Question 3

highest

lowest

negative

none of these

Solution

Question 4

Zero

One

Two

Three

Solution

Question 5

degree

constant

zero

co-efficient

Solution

Question 6

$$2$$

$$1$$

$$3$$

$$5$$

Solution

Question 7

$$p(x) = 15$$

$$p(x) = 1$$

$$p(x) = x$$

$$p(x) = 20$$

Solution

Question 8

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

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

$$p(x) = c$$

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

Solution

Question 9

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 10

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

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

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

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

Solution

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