Question

p(x) = 27x³- 54x²+3x-4;g(x)=1-3/2x By remainder theorem, fi nd the remainder when, p(x) is divided by g(x)

Answer 1

Hi ,

*****************************************
Remainder Theorem :

Let p(x) be any polynomial of degree

greater than or equal to one and let

' a ' be any real number.

If p(x) is divided by the linear

polynomial ( x - a ) , then the

remainder is p(a).

********************************************

Here ,

p(x) = 27x³-54x²+3x-4

If p(x) is divided by g(x) ,then

the remainder is p(2/3)

So ,replace x by 2/3 ,

p(2/3) = 27(2/3)³-54(2/3)²+3(2/3)-4

=27×(8/27)-54×(4/9)+2-4

= 8 - 24 + 2 - 4

= 10 - 28

= -18

Therefore ,

Required remainder = p(2/3)= -18

I hope this helps you.

: )

Answer 2

Hi,

Answer: Remainder = -18


✴️Solution:

Given polynomial

p(x) = 27x³- 54x²+3x-4

g(x)=1-3/2x

✴️To find the remainder ,find the value of x from g(x) and put that value of x in p(x)

$1 - \frac{3}{2} x = 0 \\ \\ \frac{3}{2} x = 1 \\ \\ x = \frac{2}{3}$

$p( \frac{2}{3} ) = 27 ({ \frac{2}{3} })^{3} - 54( { \frac{2}{3} })^{2} + 3 \times \frac{2}{3} - 4 \\ \\ = \frac{27 \times 2 \times 2 \times 2}{3 \times 3 \times 3} - \frac{54 \times 2 \times 2}{3 \times 3} + 2 - 4 \\ \\ = 8 - 24 + 2 - 4 \\ \\ = 10 - 28 \\ \\ = - 18$

So,remainder is -18.

Hope it helps you