Polynomials Test

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Polynomials Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

Identify the cubic polynomial.

A
$$x^5+y^3-x^3+x^4$$

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

C
$$2x^3+8y^3-9x^5$$

D
$$-7x^7+x^3$$

Solution

$$x^3+y^3-x^2$$ is the cubic polynomial.
A cubic polynomial is a polynomial of degree $$3$$.
Since the highest degree is $$3$$.
Question 2
1 / -0

A polynomial of degree ________ is called a cubic polynomial.

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

The general form of cubic polynomial is $$p(x)=ax^3+bx^2+cx+d$$ where $$x$$ is a variable and $$a,b,c,d$$ are constants. The highest power of a cubic polynomial is $$3.$$

Hence, a polynomial of degree $$3$$ is called a cubic polynomial.
Question 3
1 / -0

$$p(x) = 63 - 9x$$ is a _______ polynomial.

A
constant

B
linear

C
quadratic

D
cubic

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 $$p(x)=63-9x$$ or $$p(x)=-9x+63$$ has degree $$1$$.

Hence, the polynomial $$p(x)=63-9x$$ is a linear polynomial.
Question 4
1 / -0

Which one of the following can be an example of cubic polynomial?

A
$$x^2-x$$

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

C
$$x^3=0$$

D
$$x^5+x^4+x^3+x^2$$

Solution

A cubic polynomial is a polynomial of degree $$3$$.

Since the highest degree is $$3$$.

$$x^3=0$$ is an example of cubic polynomial.
Question 5
1 / -0

A cubic polynomial is a polynomial of degree:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

A cubic polynomial is a polynomial of degree $$3$$.
Example: $$x^3+x^2+x+1$$
Here, the highest degree is $$3$$.
Question 6
1 / -0

Find the zeroes of the linear polynomial from the graph.

A
$$A- (1.8, 0), B- (7, 0)$$

B
$$A- (2.8, 0), B- (7, 0)$$

C
$$A- (1.8, 0), B- (8, 0)$$

D
$$A- (3.8, 0), B- (7, 0)$$

Solution

From graph we can say, Polynomial A and B have zeroes at $$A- (1.8, 0), B- (7, 0)$$ respectively.
Question 7
1 / -0

$$p(x) = 25 $$ is a _______ polynomial.

A
linear

B
quadratic

C
constant

D
cubic

Solution

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

Since $$p(x)=25$$ is a polynomial with constant term $$25$$ and there is no variable in it.

Hence, $$p(x)=25$$ is a constant polynomial.
Question 8
1 / -0

Find the polynomial with degree $$6$$.

A
$$6{ x }^{ 4 }+7{ x }^{ 2 }$$

B
$$8{ x }^{ 4 }{ y }^{ 2 }+7{ x }^{ 5 }{ y }^{ 3 }-\dfrac { 3 }{ 5 } $$

C
$$8{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }+7{ x }^{ 2 }{ y }^{ 2 }z+3{ x }^{ 4 }$$

D
$$8{ x }^{ 6 }{ y }^{ 6 }+{ y }^{ 2 }+7{ x }^{ 3 }$$

Solution

In the case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.

In the case of polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.

$$(A)6x^{4}+7x^{2}$$
The highest power of this expression is 4.Then degree is 4.

$$(B)8x^{4}y^{2}+7x^{5}y^{3}-\frac{3}{5}$$
The highest power of this expression is 5+3=8. Then degree is 8.

$$(C)8x^{2}y^{2}z^{2}+7x^{2}y^{2}z+3x^{4}$$
The highest power of this expression is 2+2+2=6. Then degree is 6.

$$(D)8x^{6}y^{6}+y^{2}+7x^{3}$$
The highest power of this expression is 6+6=12. Then degree is 12.

In all option (C) is the expression with degree 6
Question 9
1 / -0

Identify the zeros of the polynomial whose graph is given

A
$$1, -1, 2$$

B
$$-2, 1, 3$$

C
$$-2, 0, 3$$

D
$$-2, 2, 3$$

Solution

the zeroes of the polynomial is when the graph cut the x-axis and in this question the graph cut the x-axis at -2 , 1 and 3
Question 10
1 / -0

Which of the following graphs is the graph of linear polynomial?

A

B

C

D

Solution

Linear polynomial represents a straight line. So Option A is correct.