Polynomials Test

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Polynomials Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Find the degree of the following polynomial:
$$-\dfrac{3}{2}$$

A
$$1$$

B
$$2$$

C
$$0$$

D
Cannot be determined

Solution

Given polynomial can be rewritten as $$-\dfrac32 x^0$$ so, the highest degree of the variable present in the polynomial is $$0$$ hence the degree of the polynomial is equal to $$0.$$
Question 2
1 / -0

Find the degree of following polynomial
$$4x-\sqrt{5}$$

A
$$\dfrac{1}{2}$$

B
1

C
2

D
0

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$4x-\sqrt{5}$$
There are 2 terms $$4p-\sqrt{5}$$,so it is a binomial and the polynomial has variable $$x$$ as the highest degree of all the terms.
Therefore,
Degree is $$1$$
Question 3
1 / -0

Find the degree of following polynomial $$5$$

A
$$5$$

B
$$1$$

C
$$0$$

D
Constant

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$5$$
Since there is $$1$$ term $$5$$, it is a monomial and the polynomial has no variable.
Therefore,
Degree is $$0$$
Question 4
1 / -0

Degree of the polynomial $$4x^4+0x^3+0x^5+5x+7$$ is

A
$$4$$

B
$$5$$

C
$$3$$

D
$$7$$

Solution

Clearly, the highest power of $$x$$ is $$4$$.
Hence, the degree of given polynomial is $$4$$.
Option A is correct.
Question 5
1 / -0

A linear polynomial

A
may have no zero

B
may have one zero

C
has one and only one zero always

D
may have more than one zero

Solution

A standard linear polynomial is given by
$$p(x)=ax+b,a\ne0$$
To find zero of $$p(x)$$, we consider
$$p(x)=0$$
$$\Rightarrow ax+b=0$$
$$\Rightarrow x=-\dfrac ba$$
$$\therefore$$ Every linear polynomial has one and only one zero.
Question 6
1 / -0

Classify $$x^3-4$$ as linear, quadratic and cubic polynomials.

A
Cubic

B
Linear

C
Quadratic

D
None of the above

Solution

The Highest power of $$x$$ in $$x^3-4$$ is $$3.$$

Therefore, $$x^3-4$$ is cubic polynomial.
Question 7
1 / -0

The degree of $$5t-\sqrt 7$$ is

A
$$5$$

B
$$1$$

C
$$7$$

D
$$0$$

Solution

Clearly, the given the given expression $$5t-\sqrt7$$ is a linear polynomial, means the highest power of $$t$$ is 1.
$$\therefore$$ degree of the given polynomial is 1.
Question 8
1 / -0

The degree of $$5x^3+4x^2+7x$$ is

A
$$1$$

B
$$2$$

C
$$4$$

D
$$3$$

Solution

$$5x^3+4x^2+7x$$
The degree is the value of the greatest exponent of any expression (except the constant ) in the polynomial.
Here, term with greatest exponent $$= 5x^3$$
exponent of this term $$=3$$
Thus, degree $$=3$$
Question 9
1 / -0

The degree of a polynomial $$x^{3} - 27$$ is

A
$$3$$

B
$$1$$

C
$$26$$

D
$$27$$

Solution

The highest power of the variable $$x$$ in the given polynomial is $$3$$.
Hence, its degree is $$3$$.
Question 10
1 / -0

The degree of the polynomial $$4x^{2} + 3x - 7$$ is:

A
$$1$$

B
$$3$$

C
$$7$$

D
$$2$$

Solution

The highest power of the variable $$x$$ in the given polynomial is $$2$$.
Hence, its degree is $$2$$.

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Polynomials Test - 25

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Polynomials Test - 25

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Question 1

$$1$$

$$2$$

$$0$$

Cannot be determined

Solution

Question 2

$$\dfrac{1}{2}$$

1

2

0

Solution

Question 3

$$5$$

$$1$$

$$0$$

Constant

Solution

Question 4

$$4$$

$$5$$

$$3$$

$$7$$

Solution

Question 5

may have no zero

may have one zero

has one and only one zero always

may have more than one zero

Solution

Question 6

Cubic

Linear

Quadratic

None of the above

Solution

Question 7

$$5$$

$$1$$

$$7$$

$$0$$

Solution

Question 8

$$1$$

$$2$$

$$4$$

$$3$$

Solution

Question 9

$$3$$

$$1$$

$$26$$

$$27$$

Solution

Question 10

$$1$$

$$3$$

$$7$$

$$2$$

Solution

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