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:
$-7 + x$
View full solution →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 $0.$
View full solution →Give an example of a binomial of degree $8.$
View full solution →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, $p(x) = x^3 - 6x^2 + 9x + 3, g(x) = x - 1.$
View full solution →What must be added to $2x^4 - 5x^3 + 2x^2 - x - 3$ 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, $p(x) = x^3 - 2x^2 - 8x - 1, g(x) = x + 1.$
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 →If $2$ and $0$ are the zeros of the polynomial $f(x)=2 x^3-5 x^2+a x+b$ 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 $\left(x^4+a x^3-7 x^2-8 x+b\right)$ is exactly divisible by $(x+2)$ as well as $(x+3)$.
View full solution →If $p(x) = 5 - 4x + 2x^2$, find:
$i. p(0)$
$ii. p(3)$
$iii. p(-2)$
View full solution →Without actual division, prove that $2x^4 - 5x^3 + 2x^2 - x + 2$ is divisible by $x^2 - 3x + 2.$
View full solution →Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when $p(x) = 2x^4 + x^3 - 8x^2 - x + 6, g(x) = 2x - 3$
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 $\left(x^4+1\right)$ is divided by $(x-1)$. Verify that remainder $=f(1)$.
View full solution →