Which of the following is an algebraic identity?

1

(a)

\((x+y)^2=x^2-2xy+y^2\)

(b)

\((x+y)^2=x^2+2xy-y^2\)

(c)

\((x+y)^2=x^2+2xy+y^2\)

(d)

\((x+y)^2=-x^2+2xy+y^2\)

The expansion for \((x-y)^2\) is

1

(a)

\(x^2-2xy+y^2\)

(b)

\(x^2+2xy+y^2\)

(c)

\(x^2+y^2\)

(d)

\(x^2-y^2\)

The compact form of (x+y)(x-y) is

1

(a)

\(x^2+y^2\)

(b)

\(x^2-2xy+y^2\)

(c)

\(x^2+2xy+y^2\)

(d)

\(x^2-y^2\)

Select the correct statement from the following:

1

(a)

Degree of a zero polynomial is zero.

(b)

Degree of a zero polynomial is not defined.

(c)

Degree of a constant polynomial is not defined

(d)

Zero of the polynomial is not defined

The number 0 is called a

1

(a)

zero polynomial

(b)

binomial

(c)

trinomial

(d)

linear polynomial

Degree of the polynomial \(p(x)=4x^4+2x^3+x^5+2x+7\) is:

1

(a)

7

(b)

4

(c)

5

(d)

3

The degree of the polynomial \(2-y^2-y^3+2y^7\) is:

1

(a)

2

(b)

7

(c)

0

(d)

3

Degree of polynomial \((x^3+5)(4-x^5)\) is:

1

(a)

0

(b)

5

(c)

3

(d)

2

The degree of the polynomial \((x^3+5)(4-x^5)\) is:

1

(a)

5

(b)

3

(c)

8

(d)

2

The degree of the polynomial \(p(x)=(x-7)^3-x^3\) is:

1

(a)

3

(b)

2

(c)

1

(d)

0

Write the expression which represents polynomial.

1

(a)

\(\sqrt { 3 } { x }^{ 2 }-x-1\)

What is the degree of a zero polynomial?

1

(a)

Not defined.

Name the degree of the polynomial -3x+2.

1

(a)

Linear polynomial.

What is x+\(\frac { 1 }{ x } \)?

1

(a)

Not a polynomial.

Write an example of a constant polynomial.

1

(a)

Constant polynomial is 7.

Write the coefficient of x³ of the following polynomials:
\(\frac { 2 }{ 3 } -\frac { 5 }{ 4 } x+{ x }^{ 3 }+\frac { 1 }{ 2 } { x }^{ 2 }\)

2

(a)

 

Point out which of the following polynomials are monomials, binomials or trinomials?
8

2

(a)

Find a zero of the polynomial p(x)=2x+1

2

(a)

\(-\frac{1}{2}\)

Chech whether -2 and 2 are zeroes of the polynomial x+2.

2

(a)

-2 is a zero but 2 is not.

Verify whether 2 and 0 are zeroes polynomial \(x^2-2x\)

2

(a)

2 and 0, both are zeros of the polynomial.

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
\({ 4x }^{ 2 }-3x+7\)

3

(a)

Write the degree of the following polynomials:
4 - y²

3

(a)

Classify the following as linear, quadratic and cubic polynomials:
y + y² + 4

3

(a)

Verify whether the following are zeroes of the polynomial, indicated against them.
\(p(x)=3x+1,x=-\frac { 1 }{ 3 } \)

3

(a)

Find the zero of the polynomial in each of the following cases: \(p(x)=x+5\)

3

(a)

Write the various coefficients in the following polynomials:
1 - 2y + 3y⁶

5

(a)

Prove that \((a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)\)=\(2(a^3+b^3+c^3-3abc)\)

5

(a)