Question Bank
Explore the world of Polynomials, understanding their types, degrees, and operations to solve algebraic expressions and equations effectively.
Question Bank for Polynomials
A polynomial of degree 3 is known as
Is it true or false that the zeroes of the polynomial p(x) = x² − 5x + 6 are 2 and 3?
If α and β are the zeroes of the polynomial ax² + bx + c, then α + β =
Which of the following is not a polynomial?
The graph of a quadratic polynomial is always a straight line.
What is the value of p(x) = x² + 2x + 1 at x = -1?
Which of the following polynomials has only one distinct zero?
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Define a polynomial and give an example.
What is the degree of a polynomial? Provide an example.
Differentiate between a monomial, binomial, and trinomial with examples.
Explain the concept of zero polynomial.
Find the value of 'k' if the polynomial 3x^2 + kx - 5 is a perfect square trinomial.
Factorize the polynomial x^2 - 4.
Solve the equation 2x^2 + 5x - 3 = 0 using the quadratic formula.
Determine the number of zeros of the polynomial 2x^3 - 5x^2 + 3x - 1.
Find the remainder when the polynomial 3x^4 - 2x^3 + 5x^2 - 7x + 4 is divided by (x - 2).
Differentiate between a monomial, binomial, and trinomial.
Explain the concept of zero polynomial with an example.
Find the remainder when the polynomial 3x^3 - 4x^2 + 5x - 2 is divided by (x - 1).
Simplify (2x^2 + 3x - 1) ÷ (x + 2).
State and prove the Remainder Theorem for polynomials.
Find the value of 'a' if (x - a) is a factor of the polynomial x^3 - 3x^2 + 2x + 6.
Determine the sum and product of the zeros of the polynomial 4x^2 - 7x + 3.
Factorize the polynomial x^4 - 16.
Solve the inequality x^2 - 4 < 0.
Find the value of 'p' if (x + 2) is a factor of the polynomial x^3 + px^2 - 4x - 8.
Determine the value of 'm' if the polynomial 2x^3 - 5x^2 + mx - 3 is divisible by (x - 2).
Simplify (3x^2 + 4x - 2) ÷ (x - 1).
State and prove the Factor Theorem for polynomials.
Find the value of 'b' if (x - b) is a factor of the polynomial x^3 - 4x^2 + 3x + 6.
Determine the sum and product of the zeros of the polynomial 3x^2 - 5x - 2.
Factorize the polynomial x^3 - 8.
Solve the inequality 2x^2 + 3x - 2 > 0.
Find the value of 'q' if (x - 3) is a factor of the polynomial x^3 - 6x^2 + qx - 9.
Determine the value of 'n' if the polynomial 4x^3 - 9x^2 + nx - 6 is divisible by (x + 1).
Find the value of x in the polynomial 3x^2 - 5x + 2 when the polynomial is equal to zero.
Determine the number of zeros of the polynomial 2x^3 - 6x^2 + 4x.
Find the sum of the zeros of the polynomial 3x^2 - 7x + 2.
Simplify the expression (2x^3 + 3x^2 - 5x) - (x^3 - 2x^2 + 4x).
Evaluate the polynomial 4x^2 - 2x + 7 for x = 3.
Determine the product of the polynomials (x + 3) and (x - 2).
Solve the equation x^2 + 6x + 9 = 0 by completing the square method.
Find the remainder when the polynomial 2x^3 - 5x^2 + 3x - 7 is divided by (x - 2).
Determine the value of k if (x - 2) is a factor of the polynomial x^2 - kx + 2.
Simplify the expression (3x^2 + 4x - 5) + (2x^2 - 3x + 1).
Factorize the polynomial 4x^2 - 9.
Solve the equation 3x^2 - 2x - 5 = 0 using the factorization method.
Find the value of p if (x + p) is a factor of the polynomial x^2 + 5x + p.
Determine the sum of the cubes of the zeros of the polynomial x^3 - 6x^2 + 11x - 6.
Simplify the expression (2x^3 + 3x^2 - 5x) + (x^3 - 2x^2 + 4x).
Solve the equation 4x^2 - 12x + 9 = 0 by using the quadratic formula.
Find the remainder when the polynomial 3x^3 - 7x^2 + 4x - 2 is divided by (x + 1).
What is the degree of the polynomial - x⁶ - 7x⁵ + 16x⁴ - 14x³ - 5x² + 17x - 6
What is the value of p(x) = x² - 3x - 4 at x = -1?
What is the zero of the linear polynomial p(x) = ax + b?
The polynomial 𝑥³ + 5𝑥 − 2 is a {{ }} polynomial and the polynomial 4𝑥² − 9 is a {{ }} polynomial.
Calculate and match the Polynomial with its value at x = k 3x³ – 2x² + x – 1
Look at the attached graph image in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x)
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case
Find the zeroes of the quadratic polynomial p(x) = x² + 7x + 10, and verify the relationship between the zeroes and the coefficients.
Find the zeroes of the polynomial 𝑥² − 3 and verify the relationship between the zeroes and the coefficients.
Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively
Verify that 3, –1, and –⅓ are the zeroes of the cubic polynomial p(x) = 3x³ – 5x² – 11x – 3, and then verify the relationship between the zeroes and the coefficients.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 𝑥² − 2𝑥 − 8
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4𝑠² − 4𝑠 + 1
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 6𝑥² − 3 − 7𝑥
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4𝑢² + 8𝑢
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 𝑡² − 15
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 3𝑥² − 𝑥 − 4
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 1⁄4, -1
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. √2, 1/3
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 0, √5
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 1, 1
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. -1⁄4, 1/3
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 4, 1
