Which one of the following is a polynomial?
\(\dfrac{x^2}{2} - \dfrac{2}{x^2}\)
\(\sqrt{2x} - 1\)
\(x^2 + \dfrac{3x^{3/2}}{\sqrt{x}}\)
\(\dfrac{x-1}{x+1}\)
\(\sqrt{2}\) is a polynomial of degree
2
0
1
\(\dfrac{1}{2}\)
Degree of the polynomial \(4x^4 + 0x^3 + 0x^5 + 5x + 7\) is
4
5
3
7
Degree of the zero polynomial is
0
1
Any natural number
Not defined
If \(p(x)=x^2-2\sqrt{2}\,x+1\), then \(p(2\sqrt{2})\) is equal to
0
1
\(4\sqrt{2}\)
\(8\sqrt{2}+1\)
The value of the polynomial \(5x-4x^2+3\), when \(x=-1\), is
-6
6
2
-2
If \(p(x)=x+3\), then \(p(x)+p(-x)\) is equal to
3
\(2x\)
0
6
Zero of the zero polynomial is
0
1
Any real number
Not defined
Zero of the polynomial \(p(x)=2x+5\) is
\(-\dfrac{2}{5}\)
\(-\dfrac{5}{2}\)
\(\dfrac{2}{5}\)
\(\dfrac{5}{2}\)
One of the zeroes of the polynomial \(2x^2+7x-4\) is
2
\(\dfrac{1}{2}\)
\(-\dfrac{1}{2}\)
-2
If \(x^{51}+51\) is divided by \(x+1\), the remainder is
0
1
49
50
If \(x+1\) is a factor of the polynomial \(2x^2+kx\), then the value of \(k\) is
-3
4
2
-2
\(x+1\) is a factor of the polynomial
\(x^3+x^2-x+1\)
\(x^3+x^2+x+1\)
\(x^4+x^3+x^2+1\)
\(x^4+3x^3+3x^2+x+1\)
One of the factors of \((25x^2-1)+(1+5x)^2\) is
\(5+x\)
\(5-x\)
\(5x-1\)
\(10x\)
The value of \(249^2-248^2\) is
\(1^2\)
477
487
497
The factorisation of \(4x^2+8x+3\) is
\((x+1)(x+3)\)
\((2x+1)(2x+3)\)
\((2x+2)(2x+5)\)
\((2x-1)(2x-3)\)
Which of the following is a factor of \((x+y)^3-(x^3+y^3)\)?
\(x^2+y^2+2xy\)
\(x^2+y^2-xy\)
\(xy^2\)
\(3xy\)
The coefficient of \(x\) in the expansion of \((x+3)^3\) is
1
9
18
27
If \(\dfrac{x}{y}+\dfrac{y}{x}=-1\) \((x, y \ne 0)\), the value of \(x^3-y^3\) is
1
-1
0
\(\dfrac{1}{2}\)
If \(49x^2-b=(7x+\dfrac{1}{2})(7x-\dfrac{1}{2})\), then the value of \(b\) is
0
\(\dfrac{1}{\sqrt{2}}\)
\(\dfrac{1}{4}\)
\(\dfrac{1}{2}\)
If \(a+b+c=0\), then \(a^3+b^3+c^3\) is equal to
0
\(abc\)
\(3abc\)
\(2abc\)