Question

find the remainder when x4+x3-2x2+x+1 is divided by x-1

Answer 1

Answer:

$\text{The remainder when }x^4+x^3-2x^2+x+1\text{ is divided by x-1 is 2}$

Step-by-step explanation:

Given the polynomial

$P(x)=x^4+x^3-2x^2+x+1$

we have to find the remainder when above polynomial is divided by (x-1).

By remainder theorem

$P(x)=x^4+x^3-2x^2+x+1$

$P(1)=(1)^4+(1)^3-2(1)^2+1+1$

$P(1)=1+1-2+2$

$P(1)=2$

Hence, the remainder is 2

∴ $\text{The remainder when }x^4+x^3-2x^2+x+1\text{ is divided by x-1 is 2}$

Answer 2

Answer:

Remainder = 2

Step-by-step explanation:

Remainder Theorem:

If p(x) be any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a),then the remainder is p(a).

Here ,

p(x)=x⁴+x³-2x²+x+1,

Now,

p(x) is divided by (x-1) then the remainder is p(1)

p(1) = 1⁴+1³-2(1)²+1+1

= 1+1-2+1+1

= 4-2

= 2

Therefore,

Remainder = 2

•••♪