# Free Polynomials 01 Practice Test - 10th Grade

Which of the following is a polynomial in 1 variable?

A.

4x + 2

B.

1(x+1)

C.

4x + 2 = 0

D.

x + y

#### SOLUTION

Solution : A

A polynomial is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied with one or more variables raised to a non-negative integral power . For example, (a+bx+cx2) where a, b and c are constants, and x is the variable.

Degree is the highest power of the variable.

4x+2 is a polynomial of degree 1.

1(x+1)=(x+1)1, the degree of this expression would not be non-negative. Thus, it is not a polynomial.

4x+2=0 is an equation and hence not a polynomial.

x+y is a polynomial in two variables, x and y.

Which of the following is not a polynomial?

A.

x+x2

B.

x+3

C.

3y+y2

D.

x

#### SOLUTION

Solution : C

All the variables of a polynomial should have whole numbers as exponents.

For x+x2,the exponents of the variable x are 1 and 2. All the exponents are whole numbers. Therefore, it is a polynomial.

In the expression 3y+y2,exponent of 3y is 13, but 13 is not a whole number. Hence, 3y+y2 is not a polynomial.

For x+3,the exponent of the variable is 1 which is a whole number. Therefore, it is a polynomial.

For x, the exponent of the variable is 1 which is a whole number. Therefore, it is a polynomial.

If p(x)=x233x+1, then the value of p(33) is 0.

A.

True

B.

False

#### SOLUTION

Solution : B

Given,p(x)=x233x+1x=33

p(33)=(33)233(33)+1p(33)=2727+1p(33)=0+1=1

Thus, the given statement is false.

The zero of p(x) = 5x - 75 is

___

#### SOLUTION

Solution :

To find the zeros of a polynomial expression, we must equate it to zero.

5x75=0

x=755

x=15

What is the remainder when 3x27x+5 is divided by (x1) ?

A.

0

B.

1

C.

2

D.

3

#### SOLUTION

Solution : B

Given f(x)3x27x+5
To find the remainder when it is divided by (x1), we use remainder theorem.

Remainder of f(x)(xa) is f(a).

f(1)=37+5=1
The remainder when 3x27x+5 is divided by (x1) is 1.

What is the coefficient of z in (z5)3?

A.

125

B.

-25

C.

5

D.

75

#### SOLUTION

Solution : D

(z5)3=z3533×z2×5+3×z×52

[Using (ab)3=a3b33a2b+3ab2]

(z5)3 = z312515z2+75z

Hence, the coefficient of z is 75.

Which of the following is a factor of
(x+y)3(x3+y3)?

A.

x22xy+y2

B.

xy2

C.

3xy

D.

x2+xy+y2

#### SOLUTION

Solution : C

Let P(x)=(x+y)(x+y)2(x+y)(x2xy+y2)

=(x+y)(x2+2xy+y2)(x+y)(x2xy+y2)

=(x+y)(x2+2xy+y2x2+xyy2)

[Taking (x+y) as common]

=(x+y)(3xy)

Hence, from the given options 3xy is a factor of the given polynomial.

Which of the following are polynomials?

A.

y3+4y

B.

2x1

C.

x+1x1

D.

z3+z

#### SOLUTION

Solution : B and D

The exponents of the variables of a polynomial should be a whole number.

In y3+4y=y3+4y1, the exponent of y in  (4y1) is -1 which is not a whole number.

In 2x1, the exponent of  x is a whole number.

In x+1x1=(x+1)×(x1)1, the exponent of x in (x+1)1 is not a whole number.

In z3+z, the exponents of z in both the terms is a whole number exponent.

Hence,  z3+z and 2x1 are polynomials .

Which of the following is a zero of (49x21)+(1+7x)2 ?

A. 17
B. 1
C. 17
D. 1

#### SOLUTION

Solution : A

Given,(49x21)+(1+7x)2=((7x)212)+(1+7x)2=(7x1)(7x+1)+(1+7x)(1+7x)=(1+7x)(7x1+1+7x)[Taking (1+7x) common]=(1+7x)(14x)

To find the zeroes of a polynomial expression, we must equate it to zero.(1+7x)(14x)=0(1+7x)=0;  (14x)=0x=17,0Zeroes are 17 & 0.

A polynomial y=f(x) when represented on graph cuts xaxis at 2 points and yaxis at 3 points. What is the number of zeroes of f(x) ?

A. 0
B. 3
C. 5
D. 2

#### SOLUTION

Solution : D

The zeroes of a polynomial are the points which cuts the xaxis  on the graph. As f(x) cuts xaxis at 2 points, the number of zeroes are 2.