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 $p(x) = 5x - 4x^2 + 3$ 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 $p(x) = x^2 - 3x$ are:
- A
$0, 0$
- ✓
$0, 3$
- C
$0, -3$
- D
$3, -3$
Answer: B.
View full solution →When $p(x) = x^3 - ax^2 + x$ is divided by $(x - a),$ the remainder is:
Answer: B.
View full solution →The zeros of the polynomial $p(x) = 2x^2 + 7x - 4$ are:
- A
$4,\frac{-1}{2}$
- B
$4,\frac{1}{2}$
- ✓
$-4,\frac{1}{2}$
- D
$-4,\frac{-1}{2}$
Answer: C.
View full solution →Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following: $1 - y - y^3$
View full solution →Which of the following expressions are polynomials? In case of a polynomial, write its degree.
1
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{1}{2\text{x}^2}$
View full solution →Determine the degree of the following polynomials.
$-\frac{1}{2}\text{x}+3$
View full solution → Find the zero of the polynomial:q(x) = 4x
Give an example of a binomial of degree $8.$
View full solution →Using factor theorem, show that g(x) is a factor of p(x), when $\text{p}(\text{x})=2\sqrt2\text{x}^2+5\text{x}+\sqrt2,$ $\text{g}(\text{x})=\text{x}+\sqrt2$
View full solution →Give an example of a monomial of degree 0.
Find the value of a for which $(x + 1)$ is a factor of $(ax^3 + x^2 - 2x + 4a - 9).$
View full solution →Verify that: $1$ and $2$ are the zeros of the polynomial $p(x) = x^2 - 3x + 2.$
View full solution →Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x),$ where,
$p(x) = 2x^3 + 3x^2 - 11x - 3, \text{g}(\text{x})=\Big(\text{x}+\frac{1}{2}\Big).$
View full solution →Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x),$ where,
$p(x) = 2x^3 + x^2 - 15x - 12, g(x) = x + 2.$
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 →If $p(y) = 4 - 3y -y^2 + 5y^3,$ find:
$i.\ p(0)$
$ii.\ p(2)$
$ii.\ p(-1)$
View full solution →If $p(x) = 5 - 4x + 2x^2,$ find:
$i.\ p(0)$
$ii.\ p(3)$
$iii.\ p(-2)$
View full solution →If $f(t) = 4t^2 - 3t + 6,$ find:
$i.\ f(0)$
$ii.\ f(4)$
$iii.\ f(-5)$
View full solution →If both $(x - 2)$ and $\Big(\text{x}-\frac{1}{2}\Big)$ are factors of $px^2 + 5x + r,$ prove that $p = r.$
View full solution →If $p(x) = x^3 - 3x^2 + 2x,$ find $p(0), p(1), p(2).$ What do you conclude?
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 $(x^3 - 10x^2 + ax + b)$ is exactly divisible by $(x - 1)$ as well as $(x - 2).$
View full solution →Without actual division, show that $(x^3 - 3x^2 - 13x + 15)$ is exactly divisible by $(x^2 + 2x - 3).$
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 →