A polynomial in 'x' is divided by (x - a) and for (x - a) to be a factor of this polynomial, the remainder should be :

1. -a

2. 0

3. a

4. 2a

Given f(x) = ax² + bx + c, a ≠ 0, b, c ∈ R.

Assertion (A): The factorisation of ax² + bx + c is possible only if its discriminant = b² - 4ac < 0.

Reason (R): To factorise ax² + bx + c, split the coefficient of x into two real numbers such that their algebraic sum is b and their product is ac.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Given f(x) = 16x³ - 8x² + 4x + 7

Assertion (A): When we subtract 1 from f(x), the resulting polynomial is divisible by (2x + 1).

Reason (R): $f\Big(-\dfrac{1}{2}\Big)$ = 1.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Find the remainder when 2x³ - 3x² + 4x + 7 is divided by

(i) x - 2

(ii) x + 3

(iii) 2x + 1