Polynomials Test

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Polynomials Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

A quadratic polynomial

A
has the highest power equal to $$2$$

B
has the highest power equal to $$1$$

C
has the highest power equal to $$3$$

D
None of the above.

Solution

A quadratic polynomial is a polynomial of degree $$2$$.
Example: $$x^2+x+1=0$$
Here the $$x$$ has the highest power equal to $$2$$ is called quadratic equation.
Question 2
1 / -0

Which one of the following is a quadratic polynomial?

A
$$x^2+3$$

B
$$x^3+x^2+4$$

C
$$2x^4+4x^3+3x^2+6$$

D
None of the above

Solution

We know that, a $$quadratic \: polynomial$$ is a $$polynomial$$ of degree $$2$$.
Also, the degree of a polynomial is the highest power of the variable.

Hence,
$$(A)$$ The degree of $$x^2+3$$ is $$2$$.
$$(B)$$ The degree of $$x^3+x^2+4$$ is $$3$$.
$$(C)$$ The degree of $$2x^4+4x^3+3x^2+6$$ is $$4$$.

Hence, $$x^2+3$$ is a quadratic polynomial.

So, option A is correct.
Question 3
1 / -0

The highest power in the polynomial $$x^2+6x+5$$

A
$$2$$

B
$$1$$

C
$$0$$

D
None of the above

Solution

The highest power in the polynomial $$x^2+6x+5$$ is 2.
Always check the highest exponential term of the polynomial.
Question 4
1 / -0

Which of the following is NOT a quadratic polynomial?

A
$$p(x) = x^2 + 4x - 16$$

B
$$p(y) = y^2 + 8y - 10$$

C
$$p(x) = 73x - 84$$

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

Solution

$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{A polynomial is called quadratic if degree of the polynomial is}$$ $$2$$
$$\text{Clearly degree of polynomial in option 'C' is 1.}$$

$$\textbf{Hence, option 'C' is correct choice}$$
Question 5
1 / -0

Which of the following is INCORRECT?

A
$$p(x) = 5x + 5, $$ degree $$= 1$$

B
$$p(x) = 4x^4 + 4, $$ degree $$= 4$$

C
$$p(x) = x^8 , $$ degree $$= 8$$

D
$$p(x) = 9, $$ degree $$= 9$$

Solution

A polynomial is a function of the form $$f(x) = a_{n}x^{n} + a_{n−1}x^{n−1} + ... + a_{2}x^{2} + a_1x + a_0 $$
where $$a_{n}, a_{n−1} , ... a_{2} ,a_1 , a_0 $$ . are contants
and $$n$$ is a natural number.
The degree of a polynomial is the highest power of $$x$$ in its expression.
In option A, $$p(x)=5x+5$$
Highest power of $$x$$ is $$1$$
So, degree of $$p(x)$$ is $$1$$.

In option B, $$p(x)=4x^{4}+4$$
Highest power of $$x$$ is $$4$$
So, degree of $$p(x)$$ is $$4$$.

In option C, $$p(x)=x^{8}$$
Highest power of $$x$$ is $$8$$
So, degree of $$p(x)$$ is $$8$$.

Looking at Option $$D$$
$$p(x) = 9=9.x^{0}$$
Highest power of $$x$$ in $$p(x) $$ is $$=0$$
So, degree of the polynomial $$p(x)$$ is $$0$$.
Thus, it is incorrect.
Hence, the answer is option D.
Question 6
1 / -0

Find the variable of the linear polynomial $$t+5$$.

A
$$5$$

B
$$t$$

C
$$0$$

D
None of the above

Solution

Since in a polynomial $$x+a$$, $$x$$ is a variable and $$a$$ is a constant term, therefore, the linear polynomial $$t+5$$ has a variable $$t$$ and $$5$$ is a constant term.

Hence, the variable of the given linear polynomial is $$t$$.
Question 7
1 / -0

Identify linear polynomial from the following.

A
$$x+1$$

B
$$x^2+x+5$$

C
$$x^3+2x^2+6x+5$$

D
None of the above

Solution

When the degree of polynomial is $$1$$, then it is called as linear polynomial.
So, $$x + 1$$ is a linear polynomial because the degree of $$x$$ is $$1$$.
Question 8
1 / -0

The number of terms in the quadratic polynomial $$x^2+4x+4$$ is

A
$$2$$

B
$$4$$

C
$$3$$

D
None of the above

Solution

Since number of unlike terms are three hence number of terms in $$x^2+4x+4$$ is 3
Question 9
1 / -0

$$p(x) = \dfrac{37}{15}$$ is a _______ polynomial.

A
linear

B
quadratic

C
cubic

D
none of these

Solution

The general form of a constant polynomial is $$p(x)=c$$ with constant $$c$$.

Since $$p(x)=\frac { 37 }{ 15 }$$ is a polynomial with constant term $$\frac { 37 }{ 15 }$$ and there is no variable in it.

Hence, $$p(x)=\frac { 37 }{ 15 }$$ is a constant polynomial.
Question 10
1 / -0

Find the cubic polynomial with three different variables.

A
$$x^3+y^3+2^3-5^3$$

B
$$a^3+b^3-c^2+1$$

C
$$x^3+x^2+x$$

D
$$xy^2+xy^3-xy+6^3$$

Solution

A cubic polynomial is a polynomial of degree $$3$$.
$$a^3+b^3-c^2+1$$ is the cubic polynomial with three different variables $$a, b$$ and $$c$$.

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Polynomials Test - 28

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Polynomials Test - 28

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Question 1

has the highest power equal to $$2$$

has the highest power equal to $$1$$

has the highest power equal to $$3$$

None of the above.

Solution

Question 2

$$x^2+3$$

$$x^3+x^2+4$$

$$2x^4+4x^3+3x^2+6$$

None of the above

Solution

Question 3

$$2$$

$$1$$

$$0$$

None of the above

Solution

Question 4

$$p(x) = x^2 + 4x - 16$$

$$p(y) = y^2 + 8y - 10$$

$$p(x) = 73x - 84$$

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

Solution

Question 5

$$p(x) = 5x + 5, $$ degree $$= 1$$

$$p(x) = 4x^4 + 4, $$ degree $$= 4$$

$$p(x) = x^8 , $$ degree $$= 8$$

$$p(x) = 9, $$ degree $$= 9$$

Solution

Question 6

$$5$$

$$t$$

$$0$$

None of the above

Solution

Question 7

$$x+1$$

$$x^2+x+5$$

$$x^3+2x^2+6x+5$$

None of the above

Solution

Question 8

$$2$$

$$4$$

$$3$$

None of the above

Solution

Question 9

linear

quadratic

cubic

none of these

Solution

Question 10

$$x^3+y^3+2^3-5^3$$

$$a^3+b^3-c^2+1$$

$$x^3+x^2+x$$

$$xy^2+xy^3-xy+6^3$$

Solution

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