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Published on: 27/07/2018
In this chapter Polynomials contains important questions in CBSE 9th Standard Mathematics. It also covered with the most important questions in Polynomials.
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Questions + Answers key
Take MCQ Mathematics Test
1.
Determine whether the indicated numbers are zeros of the given polynomial?
\(g(x)={ 3x }^{ 2 }-2;\quad x=\frac { 2 }{ \sqrt { 3 } } ,-\frac { 2 }{ \sqrt { 3 } } \)
2.
Find the product of \((3x+2y)(3x-2y)(9x^2+4y^2)\).
3.
Find if remainder obtained on dividing polynomial \(p(x)=y^3+ay^2+5y-25\)
is a factor of polynomial \(f(a)=a^2-5a+25\).
4.
Find the value of k (k≠0), if (x-3) is a factor of \(k^2x^2-kx^2+3kx-k.\)
5.
Find the value of k, if x+2 is a factor of \(3x^2+kx+6\)
6.
If 2x-1 is a factor of \(4x^3-16x^2+10x+k\) then find the value of k.
7.
Find the value of k such that (x-1) is a factor of \(5x^3+4x^2-6x+2k.\)
8.
Verify whether 2 and 0 are zeroes polynomial \(x^2-2x\)
9.
Chech whether -2 and 2 are zeroes of the polynomial x+2.
10.
Find a zero of the polynomial p(x)=2x+1
11.
Product of \((x-\frac{1}{x})(x+\frac{1}{x})(x^2+\frac{1}{x^2})\) is:
\(x^4+\frac{1}{x^4}\)
\(x^3+\frac{1}{x^3}-2\)
\(x^4-\frac{1}{x^4}\)
\(x^2+\frac{1}{x^2}+2\)
12.
If the area of a rectangle is \(4x^2+4x-3,\) then it's possible dimensions are:
2x-3, 2x+1
2x-1, 2x+3
3x+1, 2x-3
3x-1, 2x+3
13.
Degree of polynomial \((x^3+5)(4-x^5)\) is:
0
5
3
2
14.
Degree of the polynomial \(p(x)=4x^4+2x^3+x^5+2x+7\) is:
7
4
5
3
15.
\((1+3x)^3\) is an example of:
Monomial
Binomial
Trinomial
None of these
16.
Which of the following is a polynomial?
In (a), negative power of x; in (b) and (c), fractional powers of x
\(x^2+x+\frac{3}{x^2}\)
\(\sqrt{x}+5\)
\(x^{3/4}-7x+4\)
\(\frac{3}{2}x^3-\frac{4}{3}x^2+2x-1\)
17.
Select the correct statement from the following:
Degree of a zero polynomial is zero.
Degree of a zero polynomial is not defined.
Degree of a constant polynomial is not defined
Zero of the polynomial is not defined
18.
The compact form of (x+y)(x-y) is
\((x+y)(x-y)=x^2-y^2\) is an algebraic identity
\(x^2+y^2\)
\(x^2-2xy+y^2\)
\(x^2+2xy+y^2\)
\(x^2-y^2\)
19.
The expansion for \((x-y)^2\) is
\((x-y)^2=x^2-2xy+y^2\) is an algebraic identity
\(x^2-2xy+y^2\)
\(x^2+2xy+y^2\)
\(x^2+y^2\)
\(x^2-y^2\)
20.
Which of the following is an algebraic identity?
\((x+y)^2=x^2+2xy+y^2\) is an algebraic identity
\((x+y)^2=x^2-2xy+y^2\)
\((x+y)^2=x^2+2xy-y^2\)
\((x+y)^2=x^2+2xy+y^2\)
\((x+y)^2=-x^2+2xy+y^2\)
1.
We have \(g(x)={ 3x }^{ 2 }-2\)
\(g\left( \frac { 2 }{ \sqrt { 3 } } \right) =3{ \left( \frac { 2 }{ \sqrt { 3 } } \right) }^{ 2 }-2=2\neq 0\)
\(\therefore \ x=\frac { 2 }{ \sqrt { 3 } } \)is not a zero of g(x)
\(g\left( -\frac { 2 }{ \sqrt { 3 } } \right) =3{ \left( -\frac { 2 }{ \sqrt { 3 } } \right) }^{ 2 }-2=2\neq 0\)
\(\therefore x=-\frac { 2 }{ \sqrt { 3 } } \) is not a zero of g(x)
2.
\(81x^4-16y^4\)
3.
Yes
4.
0, \(\frac{1}{27}\)
5.
9
6.
\(-\frac{3}{2}\)
7.
\(-\frac{3}{2}\)
8.
Let p(x) = x2 – 2x
Then p(2) = 22 – 4 = 4 – 4 = 0
and p(0) = 0 – 0 = 0
Hence, 2 and 0 are both zeroes of the polynomial x2 – 2x.
9.
Let p(x) = x + 2.
Then p(2) = 2 + 2 = 4, p(–2) = –2 + 2 = 0
Therefore, –2 is a zero of the polynomial x + 2, but 2 is not.
10.
\(\left(-\frac{1}{2}\right)\)
11.
\((x-\frac{1}{x})(x+\frac{1}{x})(x^2+\frac{1}{x^2})\)
\((x^2-\frac{1}{x^2})(x^2+\frac{1}{x^2})=x^4-\frac{1}{x^4}\)
12.
\((2x-1)(2x+3)=4x^2+4x-3\)
13.
Highest power of x=3+2=5
14.
Highest power of x=5
15.
\((1+3x)^3\) \(=1+27x^3+9x+27x^2\) It has 4 terms
16.
(d)
\(\frac{3}{2}x^3-\frac{4}{3}x^2+2x-1\)
17.
Convention
18.
(a)
\(x^2+y^2\)
19.
(a)
\(x^2-2xy+y^2\)
20.
(c)
\((x+y)^2=x^2+2xy+y^2\)
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