Question

find the remainder when x^4+x^3-2x^2+x+1 is divided by x-1​

Answer 1

Answer:

Reminder=2

Step-by-step explanation:

x-1) x⁴+x³-2x²+x+1( x²+x-x+1

x⁴. - x²

(-). (+)

_____________

x³-x²+x+1

x³. - x

(-). (+)

_______________

- x²+2x+1

- x²+ x

(+). (-)

_________________

x+1

x-1

(-) (+)

______________________

2

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Answer 2

☯GIVEN

• $\bf{p(x) =x^4+x^3-2x^2+x+1}$

• $\bf{g(x) = x-1}$

☯TO FIND :

• Reminder.

➲SOLUTION :

• By Remainder Theorem :

Let us assume g(x) = 0.

$: \longrightarrow{ \tt{x -1 = 0}}$

$: \longrightarrow{ \tt{x = 0 +1}}$

$: \longrightarrow{ \bf{x = 1}}$

Substituting the value of x :

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

$: \longrightarrow{\tt{p(1) =(1)^4+(1)^3-2(1)^2+1+1}}$

$: \longrightarrow{\tt{p(1) =1+1-2\times 1+1+1}}$

$: \longrightarrow{\tt{p( 1) = 1+1 -2+1 + 1}}$

$: \longrightarrow{\tt{p( 1) = 1 + 1 + 1 + 1 - 2}}$

$: \longrightarrow{\tt{p( 1) =4 - 2 }}$

$\longrightarrow{\underline{ \pink{\boxed{\bf{p( 1) = 2}}}}}$

$\huge{\green{\therefore}}$ Remainder = 2.