Polynomials Test

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Polynomials Test - 30

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Weekly Quiz Competition

Question 1
1 / -0

The degree of the polynomial $$2x^{2} - 4x^{3} + 3x + 5$$ is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

The degree of the polynomial means the highest power of the variable.
Therefore, the degree of the polynomial $$2x^2-4x^3+3x+5$$ is $$3$$.
Question 2
1 / -0

The degree of the polynomial $$5x^7 - 6x^5 + 7x - 6$$ is

A
$$4$$

B
$$5$$

C
$$6$$

D
$$7$$

Solution

The degree of a polynomial is the highest exponent of variable.
Here highest exponent is $$7$$.
So, the degree is $$7$$.
Option $$D$$ is correct.
Question 3
1 / -0

The degree of the polynomial $$x^{2} - 5x^{4} +\dfrac {3}{4}x^{7} - 73x + 5$$ is ____

A
$$7$$

B
$$\dfrac {3}{4}$$

C
$$4$$

D
$$-73$$

Solution

Given equation is $$P(x)=x^{2}-5x^{4}+\dfrac{3}{4}x^{7}-73x+5$$
We know that, the degree of a polynomial is the highest power of its variables when the polynomial is expressed in its canonical form consisting of a linear combination of monomials.
In the given equation, $$7$$ is the highest power
Then, the degree of polynomial $$P(x)$$ is $$7$$.
Question 4
1 / -0

The degree of the polynomial $$4x^2-7x^3+6x+1$$ is.

A
2

B
1

C
3

D
0

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.

Let $$p(x) = 4x^{2}-7x^{3}+6x+1$$
$$\Rightarrow$$The degree of a polynomial is the highest power of $$x$$ in its expression.

$$\Rightarrow$$Highest power of $$x$$ in $$p(x) $$ is $$=3

Thus, the degree $$=3$$

$$p(x) = 4x^{2}-7x^{3}+6x+1 $$ is a cubic polynomial.
Hence, option $$C $$ is correct.
Question 5
1 / -0

The polynomial $$3x-2$$ is a.

A
Linear polynomial

B
Quadratic polynomial

C
Cubic polynomial

D
Constant polynomial

Solution

there are no powers greater than $$1$$ therefore it is a linear polynomial
Question 6
1 / -0

The degree of $$(6{x}^{7} -7{x}^{3} + 3{x}^{2} + 2x -1)$$ is ______.

A
$$7$$

B
$$6$$

C
$$3$$

D
$$5$$

Solution

The degree is the highest power of an exponent in the polynomial.
In the given polynomial,
$$(6{x}^{7} -7{x}^{3} + 3{x}^{2} + 2x -1)$$

It can be clearly observed that the first term $$6{x}^{7}$$ has the highest power of $$x$$ i.e $$7$$.

Thus, the degree of the given polynomial is $$7$$.

Hence, $$7$$ is the correct answer.
Question 7
1 / -0

The polynomial $$4x^2+2x-2$$ is a

A
Linear polynomial

B
Quadratic polynomial

C
Cubic polynomial

D
Constant polynomial

Solution

we can see that the highest power is $$2$$ therefore it is a quadratic polynomial
Question 8
1 / -0

The degree of $$(6x^{4} - 7x^{3} + 3x^{2} + 2x - 1)$$ is _______.

A
$$4$$

B
$$6$$

C
$$3$$

D
$$5$$

Solution

Given polynomial is $$6x^4-7x^3+3x^2+2x-1$$
For the given polynomial, highest power of $$x$$ is $$4$$.
And it should be Integer,
Thus degree of polynomial is $$4$$.
Question 9
1 / -0

The degree of the polynomial $$p(x) =x^7 - 5x^3 - 3x^2 + 2x$$ is _____

A
$$7$$

B
$$2$$

C
$$3$$

D
$$1$$

Solution

Given the polynomial is $$p(x) =x^7 - 5x^3 - 3x^2 + 2x$$.
Now the power of the highest degree term is $$7$$ so the degree of the polynomial is $$7$$.
Question 10
1 / -0

The degree of the polynomial $$x^2-5x^4+\dfrac{3}{4}x^7-73x+5$$ is

A
$$7$$

B
$$\dfrac{3}{4}$$

C
$$4$$

D
$$-73$$

Solution

The degree of a polynomial is the highest degree of its monomials.
Degree of $${x}^{2}$$ is $$2$$
Degree of $$-5{x}^{4}$$ is $$4$$
Degree of $$\dfrac{3}{4}{x}^{7}$$ is $$7$$
Degree of $$-73x$$ is $$1$$
Degree of $$5$$ is $$0$$
The highest degree of the polynomial is $$7$$.

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Polynomials Test - 30

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Polynomials Test - 30

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Question 1

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 2

$$4$$

$$5$$

$$6$$

$$7$$

Solution

Question 3

$$7$$

$$\dfrac {3}{4}$$

$$4$$

$$-73$$

Solution

Question 4

2

1

3

0

Solution

Question 5

Linear polynomial

Quadratic polynomial

Cubic polynomial

Constant polynomial

Solution

Question 6

$$7$$

$$6$$

$$3$$

$$5$$

Solution

Question 7

Linear polynomial

Quadratic polynomial

Cubic polynomial

Constant polynomial

Solution

Question 8

$$4$$

$$6$$

$$3$$

$$5$$

Solution

Question 9

$$7$$

$$2$$

$$3$$

$$1$$

Solution

Question 10

$$7$$

$$\dfrac{3}{4}$$

$$4$$

$$-73$$

Solution

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