Question

p(x) = x³-3x²+4x+50;g(x)=x-3 By remainder theorem, fi nd the remainder when, p(x) is divided by g(x)

Answer 1

Hi ,

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

Remainder Theorem :

On dividing the polynomial p(x)

of degree one or more than 1

by a linear polynomial ( x - a ) ,

the remainder obtained is p(a),

where a is real number .

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

Now ,

It is given that ,

p(x) = x³-3x²+4x+50,

is divided by g(x) = x-3 ,

then the remainder is p(3)

p(3) = 3³ - 3(3)² +4(3)+50

= 27 - 27 + 12 + 50

= 62

Therefore ,

Required remainder = p(3)=62

I hope this helps you.

: )

Answer 2

Hello,

Answer: Remainder = 62

Solution:

As
$g(x) = x - 3$
So find the value of x by equating g(x)=0, and then put the value of x into p(x) to get the remainder.

$g(x) = 0 \\ \\ x - 3 = 0 \\ \\ x = 3$
$p(x) = {x}^{3} - 3 {x}^{2} + 4x + 50 \\ \\ p(3) = {3}^{3} - 3( {3})^{2} + 4 \times 3 + 50 \\ \\ = 27 - 27 + 12 + 50 \\ \\ = 62$
Thus 62 is the remainder.

Hope it helps you