Polynomials Test

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Polynomials Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

In a polynomial, the exponents of the variables are always

A
integers

B
positive integers

C
non-negative integers

D
non-positive integers

Solution

A polynomial is an algebraic expression that contains variables having whole number power.
Question 2
1 / -0

Find the degree of the polynomial $$5t+\sqrt{7}$$.

A
$$5$$

B
$$1$$

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

D
None of the above

Solution

The given polynomial is $$5t+\sqrt{7}$$

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

Identify the zero polynomial from the following.

A
$$0$$

B
$$5$$

C
$$4$$

D
$$3$$

Solution

The degree of the zero polynomial is undefined.
Example:
$$p(x) = ax^2+bx+c$$, when the constants $$a = b = c = 0$$ is considered as zero polynomial.
Question 4
1 / -0

Find the degree of $$2-y^2-y^3+2y^8$$

A
$$2$$

B
$$-1$$

C
$$3$$

D
$$8$$

Solution

Put the polynomial $$2-y^2-y^3+2y^8$$ in standard form. The term with the highest exponent should be first, and the term with the lowest exponent should be last. This will help us see which term has the exponent with the largest value. Therefore, the standard form is:

$$2y^8-y^3-y^2+2$$

The power is simply number in the exponent. In the polynomial, $$2y^8-y^3-y^2+2$$, the power of the first term is $$8$$which is the largest exponent of $$y$$ and hence it is the degree of given polynomial.
Question 5
1 / -0

Find the degree of the polynomial $$x^3+x+2$$.

A
$$3$$

B
$$2$$

C
$$1$$

D
None of the above

Solution

The degree of the polynomial $$x^3+x+2$$ is $$3$$.
Question 6
1 / -0

Find the degree of the polynomial $$4-y^2$$.

A
$$4$$

B
$$-1$$

C
$$2$$

D
None of the above

Solution

The $$degree$$ of a $$polynomial$$ is the highest degree of its $$terms$$
Here $$y^2$$ has degree of $$2$$.
Hence, the degree of the polynomial $$4-y^2$$ is $$2$$
Question 7
1 / -0

Which of the following is/are linear polynomial?

A
$$x^{2} + 2$$

B
$$x + 5$$

C
$$x^{3} + x^{2} + 9$$

D
None of the above

Solution

A polynomial of which the highest degree is $$1$$ is called a linear polynomial.
Question 8
1 / -0

Which of the following is a linear polynomial?

A
$$4x^{2} + 5$$

B
$$x + 9$$

C
$$x^{4} + x^{3} + x^{2} + 1$$

D
None of the above

Solution

Degree is the highest power of $$x$$ in a given polynomial $$P(x)$$.

Option A: Degree of $$4x^2+5 \Rightarrow 2$$
Option B: Degree of $$x+9 \Rightarrow 1$$
Option C: Degree of $$x^4+x^3+x^2+1\Rightarrow 4$$

Since, the degree of option B is $$1$$, it is a linear polynomial.
Question 9
1 / -0

$$p(x) = \dfrac{2}{3} x - \dfrac{7}{10}$$ is a __________.

A
linear polynomial

B
constant polynomial

C
quadratic polynomial

D
cubic polynomial

Solution

The general form of linear polynomial is $$p(x)=ax+b$$ where $$x$$ is a variable and $$b$$ is a constant. The first term of this polynomial has power $$1$$ and therefore, the degree of the polynomial is $$1$$.

Similarly the polynomial $$p(x)=\dfrac { 2 }{ 3 } x-\dfrac { 7 }{ 10 }$$ has degree $$1$$.

Hence, the polynomial $$p(x)=\dfrac { 2 }{ 3 } x-\dfrac { 7 }{ 10 }$$ is a linear polynomial.
Question 10
1 / -0

Find the linear polynomial.

A
$$2x+5$$

B
$$6x+2$$

C
$$9y+7$$

D
All of the above

Solution

A linear polynomial is the same thing as a $$degree$$ $$1$$ polynomial i.e after combining the degree of the terms if the highest degree is $$1$$ then it is called a linear polynomial.

Linear polynomial are defined in equation form as : $$ ax + b $$

$$\therefore$$ All of the above equations, $$2x + 5$$, $$6x+2$$ and $$ 9y + 7 $$ are linear polynomials.

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Polynomials Test - 27

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Polynomials Test - 27

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Question 1

integers

positive integers

non-negative integers

non-positive integers

Solution

Question 2

$$5$$

$$1$$

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

None of the above

Solution

Question 3

$$0$$

$$5$$

$$4$$

$$3$$

Solution

Question 4

$$2$$

$$-1$$

$$3$$

$$8$$

Solution

Question 5

$$3$$

$$2$$

$$1$$

None of the above

Solution

Question 6

$$4$$

$$-1$$

$$2$$

None of the above

Solution

Question 7

$$x^{2} + 2$$

$$x + 5$$

$$x^{3} + x^{2} + 9$$

None of the above

Solution

Question 8

$$4x^{2} + 5$$

$$x + 9$$

$$x^{4} + x^{3} + x^{2} + 1$$

None of the above

Solution

Question 9

linear polynomial

constant polynomial

quadratic polynomial

cubic polynomial

Solution

Question 10

$$2x+5$$

$$6x+2$$

$$9y+7$$

All of the above

Solution

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