Q. 53.8( 61 Votes )

# If f(x) = x^{4} – 2x^{2} + ax + b is divided by (x – 2), the remainder is 4. If (a + b) = –4. Find the value of a.

Answer :

**Concept Used:**

**Remainder theorem:** If a polynomial f(x) is divided by (x – a) then f(a) will give the remainder.

**Explanation:**

f(x) = x^{4} – 2x^{2} + ax + b

f(2) = (2)^{4} – 2(2)^{2} + a.2 + b

f(2) = 16 – 8 + 2a + b

f(2) = 8 + 2a + b

f(2) = 4

8 + 2a + b = 4

2a + b = –4

a + (a + b) = –4

a – 4 = –4

a = 0

**Hence, the value of a is 0.**

Rate this question :

In each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = 3*x*^{4}+2*x*^{3}, *g*(*x*) = *x*+

In each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = 9*x*^{3}-3*x*^{2}+*x*-5, *g*(*x*) = *x*=

If p (x) = 2x^{3} + ax^{2} + 3x – 5 and q (x) = x^{3} + x^{2} – 4x + a leave the same remainder when divided by (x – 2), show that

If (x^{3} + mx^{2} – x + 6) has (x - 2) as a factor and leaves a remainder r, when divided by (x - 3), find the values of m and r.

If (x – 2) is a factor of 2x^{3} – 7x^{2} + 11x + 5a, find the value of a.

When p (x) = x^{4} + 2x^{3} – 3x^{2} + x – 1 is divided by (x – 2), the remainder is

When p (x) = x^{3} – ax^{2} + x is divided by (x – a), the remainder is

Find the remainder when the polynomial f(x) = 4x^{2} - 12x^{2} + 14x - 3 is divided by (2x - 1).

(x +1) is a factor of the polynomial:

RS Aggarwal & V Aggarwal - MathematicsWhen p (x) = 4x^{3} - 12x^{2} + 11x – 5 is divided by (2x – 1), the remainder is