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Published on: 23/08/2019
Polynomials
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Questions + Answers key
Take MCQ Mathematics Test
1.
If \(p(x)=x^2-2\sqrt{2}x+1,\) then \(p(2\sqrt{2})\) is:
0
1
\(4\sqrt{2}\)
\(3\sqrt{2}+1\)
2.
If \(p(x)=3x-7,\) then \(p(x)+p(-x)\) is:
7
6x
0
-14
3.
If \(p(x)=7-3x+2x^2\) then value of p(-2) is:
12
31
21
22
4.
The zeros of the polynomial p(x)=(x-6)(x-5) are:
-6, -5
-6, 5
6, -5
6, 5
5.
The maximum number of zeros of the polynomial p(y)=mya is:
a+1
m
m+1
a
6.
The maximum number of terms in a polynomial of degree 10 is:
9
10
11
1
7.
The degree of the polynomial \((x^3+5)(4-x^5)\) is:
5
3
8
2
8.
Degree of polynomial \((x^3+5)(4-x^5)\) is:
0
5
3
2
9.
Degree of the polynomial \(4x^4+0x^3+0x^5+5x+7\) is:
7
5
4
3
10.
Degree of which of the following polynomials is zero?
x
15
y
\(x+\frac{1}{x}\)
11.
Which of the following is a binomial in y?
\(y^2+2\)
\(y+\frac{1}{y}+2\)
\(\sqrt{y}+\sqrt{2}y\)
\(y\sqrt{y}+1\)
12.
A linear polynomial
has one and only one zero
may have no zero
may have one zero
may have more than one zero
13.
Which of the following is a polynomial in one variable?
\(3-x^2+x\)
\(\sqrt{3x}+4\)
\(x^3+y^3+7\)
\(x+\frac{1}{x}\)
14.
The number 0 is called a
zero polynomial
binomial
trinomial
linear polynomial
15.
Which of the following is an algebraic identity?
\((x+y)^2=x^2+2xy+y^2\) is an algebraic identity
\((x+y)^2=x^2-2xy+y^2\)
\((x+y)^2=x^2+2xy-y^2\)
\((x+y)^2=x^2+2xy+y^2\)
\((x+y)^2=-x^2+2xy+y^2\)
16.
Write the factors of polynomial 4x2+y2+4xy+8x+4y+4
17.
Write the factors of a3-1.
18.
Factorize: 8y3-125x3.
19.
Factorize: 6-x+x2.
20.
Factorize: 20x2-9x+1.
21.
If f(x) be a polynomial such that \(f\left( -\frac { 1 }{ 3 } \right) \)=0, then calculate one factor of f(x).
22.
In the expression x2+\(\frac { \pi }{ 2 } x-7\), what is the co-efficient of x?
23.
What is x+\(\frac { 1 }{ x } \)?
24.
What is the degree of a zero polynomial?
25.
Write the expression which represents polynomial.
1.
\(p(x)=x^2-2\sqrt{2}x+1\)
\(\therefore\) \(p(2\sqrt{2})=(2\sqrt{2})^2-(2\sqrt{2})(2\sqrt{2})+1\)
= 0
2.
Evaluate p(-x)
3.
\(p(-2)=7-3(-2)+2(-2)^2=21\)
4.
\((x-6)(x-5)=0\quad \Rightarrow\quad\quad x=6, 5\)
5.
Evident
6.
A polynomial of degree n has maximum number of terms as (n+1)
7.
\((x^3+5)(4-x^5)\)\(=4x^3-x^8+20-5x^5\)
8.
Highest power of x=3+2=5
9.
Highest power of x=4
10.
15 is a constant polynomial
11.
\(y^2+2\) has two terms; three terms in (b) fractional power of y in (c) and (d);
12.
A characteristic of a linear polynomial
13.
Fractional power of x in (b),
Two variables in (c),
Negative power of x in (d)
14.
Definition of zero polynomial
15.
(c)
\((x+y)^2=x^2+2xy+y^2\)
16.
( )
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.
17.
( )
a3-1=(a-1)(a2+1+a\(\times\)1)
Then factors of (a3-1) are (a-1) and (a2+1+a).
18.
( )
8y3-125x3=(2y)3-(5x)3
=(2y - 5x)(4y2+10xy+25x2)
19.
( )
6x-x-x2 = 6-3x+2x-x2
= 3(2-x)+x(2-x)
= (2-x)(3+x)
20.
( )
20x2-9x+1 = 20x2-5x-4x+1
=5x(4x-1)-1(4x-1)
=(4x-1)(5x-1)
21.
( )
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).
22.
( )
Co-efficient of x in expression x2+\(\frac { \pi }{ 2 } c-7is\frac { \pi }{ 2 } \)
23.
( )
Not a polynomial.
24.
( )
Not defined.
25.
( )
\(\sqrt { 3 } { x }^{ 2 }-x-1\)
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