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 number 0 is called a

1

(a)

zero polynomial

(b)

binomial

(c)

trinomial

(d)

linear polynomial

Which of the following is a polynomial in one variable?

1

(a)

\(3-x^2+x\)

(b)

\(\sqrt{3x}+4\)

(c)

\(x^3+y^3+7\)

(d)

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

A linear polynomial

1

(a)

has one and only one zero

(b)

may have no zero

(c)

may have one zero

(d)

may have more than one zero

Which of the following is a binomial in y?

1

(a)

\(y^2+2\)

(b)

\(y+\frac{1}{y}+2\)

(c)

\(\sqrt{y}+\sqrt{2}y\)

(d)

\(y\sqrt{y}+1\)

Degree of which of the following polynomials is zero?

1

(a)

x

(b)

15

(c)

y

(d)

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

Degree of the polynomial \(4x^4+0x^3+0x^5+5x+7\) is:

1

(a)

7

(b)

5

(c)

4

(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 maximum number of terms in a polynomial of degree 10 is:

1

(a)

9

(b)

10

(c)

11

(d)

1

The maximum number of zeros of the polynomial p(y)=my^a is:

1

(a)

a+1

(b)

m

(c)

m+1

(d)

a

The zeros of the polynomial p(x)=(x-6)(x-5) are:

1

(a)

-6, -5

(b)

-6, 5

(c)

6, -5

(d)

6, 5

If \(p(x)=7-3x+2x^2\)  then value of p(-2) is:

1

(a)

12

(b)

31

(c)

21

(d)

22

If \(p(x)=3x-7,\) then \(p(x)+p(-x)\) is:

1

(a)

7

(b)

6x

(c)

0

(d)

-14

If \(p(x)=x^2-2\sqrt{2}x+1,\) then \(p(2\sqrt{2})\) is:

1

(a)

0

(b)

1

(c)

\(4\sqrt{2}\)

(d)

\(3\sqrt{2}+1\)

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.

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

1

(a)

Not a polynomial.

In the expression x²+\(\frac { \pi }{ 2 } x-7\), what is the co-efficient of x?

1

(a)

Co-efficient of x in expression x²+\(\frac { \pi }{ 2 } c-7is\frac { \pi }{ 2 } \)

If f(x) be a polynomial such that \(f\left( -\frac { 1 }{ 3 } \right) \)=0, then calculate one factor of f(x).

1

(a)

Since, \(f\left( -\frac { 1 }{ 3 } \right) \) =0
\(\therefore -\frac { 1 }{ 3 } \) is a zero of polynomial f(x)
So, x+\(\frac { 1 }{ 3 } \)or 3x+1 is a factor of f(x).

Factorize: 20x²-9x+1.

1

(a)

20x²-9x+1 = 20x²-5x-4x+1
=5x(4x-1)-1(4x-1)
=(4x-1)(5x-1)

Factorize: 6-x+x².

1

(a)

6x-x-x² = 6-3x+2x-x²
= 3(2-x)+x(2-x)
= (2-x)(3+x)

Factorize: 8y³-125x³.

1

(a)

8y³-125x³=(2y)³-(5x)³
=(2y - 5x)(4y²+10xy+25x²)

Write the factors of a³-1.

1

(a)

a³-1=(a-1)(a²+1+a\(\times\)1)
Then factors of (a³-1) are (a-1) and (a²+1+a).

Write the factors of polynomial 4x²+y²+4xy+8x+4y+4

1

(a)

4x²+y²+4xy+8x+4y+4 = (2x)²+(y)²+(2)²+2\(\times\)2x\(\times\)y+2\(\times\)2x\(\times\)2+2\(\times\)y\(\times\)2
= (2x+y+2)².
Factor is 2x + y + 2.