Answer :

Let, f(x) = 3x^{4} – 6x^{2} - 8x + 2

Now,

As per the question,

x – 2 = 0

x = 2

Using Remainder theorem,

We know that when f(x)is divided by (x – 2), the remainder so obtained will be f(2).

Hence,

f(2) = 3(2)^{4} – 6(2)^{2} - 8(2) + 2

= 3(16) – 6(4) -16 + 2

= 48 -24 – 14

= 10

Therefore,

The required remainder is 10.

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is divided by (x-a)

RS Aggarwal & V Aggarwal - MathematicsIn each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = 4*x*^{3}-12*x*^{2}+14*x*-3, *g*(*x*) = 2*x*-1

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

*f*(*x*) = *x*^{3}-6*x*^{2}+2*x*-4, *g*(*x*) = 1-2*x*

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

*f*(*x*) = 2*x*^{4}-6*x*^{3}+2*x*^{2}-*x*+2, *g*(*x*) = *x*+2

When (x^{31} + 31) is divided by (x + 1), the remainder is

is divided by (3x+2)

RS Aggarwal & V Aggarwal - MathematicsFind the remainder when p (x) = 4x^{3} + 8x^{2} – 17x + 10 is divided by (2x – 1).

Show that:

(i) 𝑥 + 3 is a factor of 69 + 11𝑥−𝑥^{2} + 𝑥^{3}.

(ii) 2𝑥−3 is a factor of 𝑥 + 2𝑥^{3} – 9𝑥^{2} + 12

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

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