Question

using remainder theorem , find the remainder when x^4 - 3x^3 + 2x^2 + x - 1 is divided by (x-2)

Answer 1

$\mathbb{ SOLUTION }$ :

Let,
given polynomial be

$p(x) = {x}^{4} - 3 {x}^{3} + 2 {x}^{2} + x - 1 \: \: \: .........(i)$

and g(x) = (x - 2)

Then,

P(x) is divided by g(x)

For finding the zero of g(x), put g(x) = 0

$\therefore$ x - 2 = 0
=> x = 2

So,
it is the zero of g(x).

On putting (x - 2) in [ Equation.(i) ] , we get

$p(2) = {2}^{4} - 3 {(2)}^{3} + 2 {(2)}^{2} + 2 - 1 \\ \\ \: \: \: \: \: \: \: \: \: = 16 - 24 + 8 + 1 \\ \\ \: \: \: \: \: \: \: \: = 1$

Hence, the value of p(2) is 1, which is the required remainder obtained on dividing.

Answer 2

Given polynomial :

p(x) = x⁴-3x³+2x²+x-1

Divisor = (x-2)

Consider (x-2) = 0

x=2

Now put x=2

x⁴-3x³+2x²+x-1

= (2)⁴-3(2)³+(2)²-1

= 16-24+8-1

= 1

The required remainder is = 1.

★ AhseFurieux ★