Polynomials
Practice quiz on polynomial concepts including terminology, zeros, division, and remainder theorem for classes 9 to 12
Questions
A trinomial is a polynomial with exactly how many terms?
- 3
- 4
- 5
- 6
What is called a polynomial with exactly 2 terms?
- binomial
- degree
- linear
- square
How many 0s can a polynomial of degree n have?
- 1 zero
- n zero
- 2 zero
- n-1 zero
What is the degree of the remainder atmost, when a fourth degree polynomial is divided by a quadratic polynomial?
- $2$
- $0$
- $4$
- $1$
If on dividing a non-zero polynomial $p(x)$ by a polynomial $g (x)$, the remainder is zero, what is the relation between the degrees of $p(x)$ and $g (x)$?
- degree of $g (x) \ge$ degree of $p(x)$
- degree of $g(x) \le$ degree of $p(x)$
- degree of $g (x) =$ degree of $p(x)$
- Can't say
If the polynomial $x^3-x^2+x-1$ is divided by $x-1$, then the quotient is :
- $x^2-1$
- $x^2+1$
- $x^2-x+1$
- $x^2+x+1$
When the polynomial ${x^4} + {x^2} + 1$ is divided by $(x + 1)({x^2} - x + 1)$ then the remainder is $ax + b$ , then $a + b$ is equal to
- $1$
- $2$
- $3$
- $4$
Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder.
$p(x)=x^4-3x^2+4x+5$
$g(x)=x^2+1-x$
- $q(x)=x^2+x-3$ and $r(x)=-8$
- $q(x)=x^2-x+3$ and $r(x)=8$
- $q(x)=x^2+x-3$ and $r(x)=8$
- $q(x)=x^2-x-3$ and $r(x)=-8$
On dividing $f(x)$ by a polynomial $x-1-x^2$, the quotient $q(x)$ and remainder $r(x)$ are $(x-2)$ and $3$ respectively. Then $f(x)$ is
- $f(x)=-3x^2-x+7$
- $f(x)=-x^3+x^2-x+7$
- $f(x)=3x^2-3x+5$
- $f(x)=-x^3+3x^2-3x+5$
On dividing $x^3-3x^2+x+2$ by a polynomial $g(x)$, the quotient and remainder were $(x-2)$ and $(-2x+4)$, respectively. Find $g(x)$.
- $2x^2+2x-8$
- $x^2+2x-7$
- $x^2-x+1$
- $2x^2-x+2$
On dividing $f(x)=2x^5+3x^4+4x^3+4x^2+3x+2$ by a polynomial $g(x)$, where $g(x)=x^3+x^2+x+1$, the quotient obtained as $2x^2+x+1$. Find the remainder $r(x)$.
- $r(x)=7x^3+x^2-1$
- $r(x)=3x^2+2x+1$
- $r(x)=x-2$
- $r(x)=x+1$
If the polynomial $f(x)=x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2-2x+k$, the remainder comes out to be $(x+a)$, then values of $k$ and $a$ are
- $k=-2$ & $a=4$
- $k=5$ & $a=-5$
- $k=-3$ & $a=-7$
- None of these
A polynomial when divided by $\displaystyle \left ( x-6 \right )$ gives a quotient $\displaystyle x^{2}+2x-13$ and leaves a remainder $-8$. Then polynomial is
- $\displaystyle x^{3}+4x^{2}+25x-78$
- $\displaystyle x^{3}-4x^{2}-25x+70$
- $\displaystyle x^{3}-4x^{2}-25x-70$
- $\displaystyle x^{3}+4x^{2}-25x+78$
The remainders of polynomial f(x) when divided by x-1, x-2 are 2,3 then the remainder of f(x) when divided by (x-1) (x-2) is
- 2x-1
- x-1
- 2x+1
- x+1
If the remainders of the polynomial f(x) when divided by x+1 and x-1 are 3, 7 then the remainder of f(x) when divided by $(x^{2} -1 )$ is
- x + 4
- 2x + 3
- 2x + 4
- 2x + 5