Sample QuestionsPolynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $p(x)=5 x-4 x^2+3$ then $p(-1)=$ ?
Answer: D.
View full solution →Which of the following is a linear polynomial?
Answer: B.
View full solution →The zeros of the polynomial $p(x)=x^2-3 x$ are:
- A
$0, 0$
- ✓
$0, 3$
- C
$0, -3$
- D
$3, -3$
Answer: B.
View full solution →When $p(x)=x^3-a x^2+x$ is divided by $(x-a)$, the remainder is:
Answer: B.
View full solution →Where $p(x)=x^4+2 x^3-3 x^2-1$ is divided by $(x-2)$, the remainder is:
Answer: D.
View full solution →Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
$-6 x^2$
View full solution →Which of the following expressions are polynomials? In case of a polynomial, write its degree.$\text{x}^5-2\text{x}^3+\text{x}+\sqrt3$
View full solution →Write:
The cofficient of x in $\sqrt3-2\sqrt2\text{x}+6\text{x}^2.$
View full solution →Which of the following expressions are polynomials? In case of a polynomial, write its degree.$\text{x}^{100}-1$
View full solution →Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
-7 + x
Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when
$p(x)=x^3-8, g(x)=x-2$
View full solution →Give an example of a monomial of degree 0.
Give an example of a binomial of degree 8.
Find the value of a for which $(x+1)$ is a factor of $\left(a x^3+x^2-2 x+4 a-9\right)$.
View full solution →Verify that:
1 and 2 are the zeros of the polynomial $p(x)=x^2-3 x+2$.
View full solution →Using the remainder theorem, find the remainder, when $p(x)$ is divided by$g(x)$,
where, $p(x)=2 x^3+x^2-15 x-12, g(x)=x+2$.
View full solution →Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where,
$p(x)=x^3-6 x^2+9 x+3, g(x)=x-1$.
View full solution →What must be added to $2 x^4-5 x^3+2 x^2-x-3$ so that the result is exactly divisible by $(x-2) ?$
View full solution →Using the remainder theorem, find the remainder, when $p ( x )$ is divided by $g ( x )$, where,
$p(x)=x^3-2 x^2-8 x-1, g(x)=x+1$
View full solution →Show that $(p-1)$ is a factor of $\left(p^{10}-1\right)$ and also of $\left(p^{11}-1\right)$.
View full solution →VWithout actual division, prove that $2 x^4-5 x^3+2 x^2-x+2$ is divisible by $x^2-3 x+2$.
View full solution →Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when
$p(x)=2 x^4+x^3-8 x^2-x+6, g(x)=2 x-3$
View full solution →Find the values of $a$ and $b$ so that the polynomial $\left(x^3-10 x^2+a x+b\right)$ is exactly divisible by $(x-1)$ as well as $(x-2)$.
View full solution →Without actual division, show that $\left(x^3-3 x^2-13 x+15\right)$ is exactly divisible by $\left(x^2+2 x-3\right)$
View full solution →By actual division, find the quotient and the remainder when $(x^4 + 1)$ is divided by $(x - 1).$
Verify that remainder =$ f(1).$
View full solution →If $2$ and $0$ are the zeros of the polynomial $f(x) = 2x^3 - 5x^2 + ax + b$ then find the values of a and b.
Hint: $f(x) = 0$ and $f(0) = 0.$
View full solution →If $p(x)=x^3+x^2-9 x-9$, find $p(0), p(3), p(-3)$ and $p(-1)$. What do you conclude about the zeros of $p(x)$ ? Is 0 a zero of $p ( x )$ ?
View full solution →If $\left(x^3+a x^2+b x+6\right)$ has $(x-2)$ as a factor and leaves a remainder 3 when divided by $(x-3)$, find the values of a and b.
View full solution →Find the values of a and b so that the polynomial $(x^4 + ax^3 - 7x^2- 8x + b)$ is exactly divisible by $(x + 2)$ as well as $(x + 3).$
View full solution →If $p(x) = 5 - 4x + 2x^2$, find:
- $p(0)$
- $p(3)$
- $p(-2)$
View full solution →