Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given the polynomial

P(x)=x^4+x^3-2x^2+x+1P(x)=x4+x3−2x2+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+1P(x)=x4+x3−2x2+x+1

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

P(1)=1+1-2+2P(1)=1+1−2+2

P(1)=2P(1)=2

Hence, the remainder is 2

Answer 2

Step-by-step explanation:

$3x - 1 = 0$

$x = \frac{1}{3}$

${x}^{4} + {x}^{3} - {2x}^{2} + 2x + 1$

$\frac{1}{16} + \frac{1}{8} - 2 \frac{1}{4} + 1 + 1 = 0$

$\frac{3}{16} - \frac{1}{2} + 2 = 0$

$\frac{3}{16} - \frac{8}{16} + 2 = 0$

$\frac{ - 5}{16} + 2 = 0$

$\frac{ - 5 + 32}{16} = 0$

$\frac{27}{16}$

$\frac{27}{16} \: \: is \: the \: remainder$