Which of the following is an algebraic identity?
\((x+y)^2=x^2+2xy+y^2\) 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
\((x-y)^2=x^2-2xy+y^2\)  is an algebraic identity

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
\((x+y)(x-y)=x^2-y^2\)  is an algebraic identity

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

Which of the following is a polynomial?
In (a), negative power of x; in (b) and (c), fractional powers of x

1

(a)

\(x^2+x+\frac{3}{x^2}\)

(b)

\(\sqrt{x}+5\)

(c)

\(x^{3/4}-7x+4\)

(d)

\(\frac{3}{2}x^3-\frac{4}{3}x^2+2x-1\)

\((1+3x)^3\) is an example of:

1

(a)

Monomial

(b)

Binomial

(c)

Trinomial

(d)

None of these

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

1

(a)

7

(b)

4

(c)

5

(d)

3

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

1

(a)

0

(b)

5

(c)

3

(d)

2

If the area of a rectangle is \(4x^2+4x-3,\) then it's possible  dimensions are:

1

(a)

2x-3, 2x+1

(b)

2x-1, 2x+3

(c)

3x+1, 2x-3

(d)

3x-1, 2x+3

Product of \((x-\frac{1}{x})(x+\frac{1}{x})(x^2+\frac{1}{x^2})\)  is:

1

(a)

\(x^4+\frac{1}{x^4}\)

(b)

\(x^3+\frac{1}{x^3}-2\)

(c)

\(x^4-\frac{1}{x^4}\)

(d)

\(x^2+\frac{1}{x^2}+2\)

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.

Find the value of k such that (x-1) is a factor of \(5x^3+4x^2-6x+2k.\)

3

(a)

If 2x-1 is a factor of \(4x^3-16x^2+10x+k\) then find the value of k.

3

(a)

Find the value of k, if x+2 is a factor of \(3x^2+kx+6\)

3

(a)

Find the value of k (k≠0), if (x-3) is a factor of \(k^2x^2-kx^2+3kx-k.\)

3

(a)

Find if remainder obtained on dividing polynomial \(p(x)=y^3+ay^2+5y-25\)

is a factor of polynomial \(f(a)=a^2-5a+25\).

3

(a)

Find the product of \((3x+2y)(3x-2y)(9x^2+4y^2)\).

5

(a)

Determine whether the indicated numbers are zeros of the given polynomial?
\(g(x)={ 3x }^{ 2 }-2;\quad x=\frac { 2 }{ \sqrt { 3 } } ,-\frac { 2 }{ \sqrt { 3 } } \)

5

(a)