If x − 2 is a factor of x³ − kx − 12, then the value of k is:

(a) 3

(b) 2

(c) −2

(d) −3

Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.

Factorize completely using the Factor Theorem: 2x³ − x² − 13x − 6.

What must be subtracted from the polynomial x³ + x² − 2x + 1 so that the resulting polynomial is exactly divisible by (x − 3)? (a) −31 (b) −30 (c) 30 (d) 31

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is: (a) (x + 1) (b) (x − 1) (c) (x − 2) (d) (x − 4)

What must be added to x³ + 7x² + 3x + 2 so that the resulting polynomial is exactly divisible by x + 2? (a) −40 (b) −16 (c) 16 (d) 40

It is given that (x − 2) is a factor of 2x³ − 7x² + kx − 2. (a) Find k. (b) Hence, factorise the resulting polynomial completely.

The polynomial kx³ + 3x² − 11x − 6 leaves a remainder of 6 when divided by x + 1. (a) Find the value of k. (b) Hence, factorise the polynomial completely.

The polynomial 3x³ + 8x² − 15x + k has (x − 1) as a factor. Find the value of k. Hence, factorize the resulting polynomial completely.

If A = and B = , then the order of AB is: (a) 2 × 2 (b) 2 × 1 (c) 1 × 2 (d) AB is not possible

If A = , then A² is equal to: (a) (b) (c) (d)

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Assertion (A): The probability of getting a number greater than 6 on throwing a die is . Reason (R): The possible outcomes on throwing a die are 1, 2, 3, 4, 5 and 6. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.