Polynomials quiz

The degree of the polynomial 4x^4 + 0x^3 + 0x^5 + 5x + 7 is:

Which of these is a polynomial?

The zero of p(x) = 2x + 5 is:

A polynomial of degree 2 is called:

If p(x) = x^2 - 3x + 2, then p(1) is:

Which is a factor of x^2 - 5x + 6?

The coefficient of x^2 in 3x^3 - 7x^2 + x is:

The value of 105 x 95 using an identity is:

(x - y)^3 equals:

If x + y + z = 0, then x^3 + y^3 + z^3 equals:

Write the degree of each polynomial: 5x^2 - 3x + 2, 7 - x^3, 9. (2 marks)

Find the zeroes of p(x) = (x - 2)(x + 3). (2 marks)

Check whether x + 1 is a factor of x^3 + x^2 + x + 1. (2 marks)

Factorise 12x^2 - 7x + 1. (2 marks)

Expand (2x + 3y)^2 using an identity. (2 marks)

Factorise 9x^2 - 25y^2. (2 marks)

Evaluate 102^2 using a suitable identity. (2 marks)

Expand (x + 4)(x + 10) using an identity. (2 marks)

Write a cubic polynomial with only two terms. (2 marks)

Find the value of p(x) = 5x - 4x^2 + 3 at x = -1. (2 marks)

Factorise x^3 - 2x^2 - x + 2 using the Factor Theorem. (3 marks)

Expand (x + 2y + 4z)^2. (3 marks)

Evaluate 101^3 and 998^3 using suitable identities. (3 marks)

Find k if x - 2 is a factor of x^2 + x + k. (3 marks)

If x + y = 12 and xy = 27, find x^3 + y^3. (3 marks)

Read the passage and answer the questions. A rectangular garden has area x^2 + 7x + 12 square m. (i) Factorise the area. (ii) Write possible length and breadth. (iii) If x = 5, find the actual length, breadth and area. (5 marks)

Read the passage and answer the questions. A cube-shaped box has volume 8x^3 + 12x^2 + 6x + 1 cubic cm. (i) Write the volume as the cube of a binomial. (ii) Find the side of the box. (iii) If x = 2, find the side and volume. (5 marks)

Read the passage and answer the questions. A company's profit in lakh rupees is modelled by p(x) = -x^2 + 10x - 16, where x is the number of thousand items sold. (i) Find p(2) and p(8). (ii) What do these values tell you about the factors of p(x)? (iii) Find the profit when 5 thousand items are sold. (5 marks)

Read the passage and answer the questions. A student uses the identity x^2 - y^2 = (x + y)(x - y) to calculate quickly in her head. (i) Evaluate 52^2 - 48^2. (ii) Evaluate 98 x 102. (iii) Factorise 49x^2 - 16. (5 marks)

Read the passage and answer the questions. A cuboid-shaped water tank has volume 12ky^2 + 8ky - 20k cubic m. (i) Take out the common factor. (ii) Factorise the quadratic part. (iii) Write possible dimensions of the tank. (5 marks)

Factorise x^3 + 13x^2 + 32x + 20 using the Factor Theorem. Explain each step. (6 marks)

Prove the identity x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) by expanding the right side. Use it to factorise 27x^3 + 8y^3 + z^3 - 18xyz. (6 marks)

Draw a diagram of a square of side (x + y) divided into parts to show (x + y)^2 = x^2 + 2xy + y^2. Use the identity to evaluate 1003^2. (6 marks)

Expand (i) (3x - 2y)^3 (ii) (2x - y + z)^2, and verify (i) by putting x = 1 and y = 1. (6 marks)

Classify polynomials by degree and number of terms using a chart with examples. Explain why x^2 + 2/x and sqrt(x) + 1 are not polynomials. (6 marks)