Question

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

Answer 1

p(x) = x⁴+ x³-2x²+ x + 1

By Remainder Theorem :

x - 1 = 0

x = 1

p(x) = x⁴+ x³-2x²+ x + 1

p(1) = (1)⁴ + (1)³ - 2(1)² + (1) +1

p(1) = 1 + 1 - 2 + 1

p(1) = 3 - 2

p(1) = 1

Remainder = 1

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Answer 2

The remainder is 2; when x⁴+ x³-2x²+ x + 1 is divided by x-1.

Given:

• Two polynomials.
• x⁴+ x³-2x²+ x + 1
• x-1

To find:

• Find the remainder when x⁴+ x³-2x²+ x + 1 is divided by x-1.

Solution:

Theorem\Concept to be used:

Remainder Theorem: When a polynomial p(x) is divided by x-a, then remainder is given by p(a); i.e. value of polynomial at x=a.

Step 1:

Find value of x from x-1.

So,

$x - 1 = 0$

Thus,

$\bf x = 1$

Step 2:

Put the value of x in p(x).

Let $p(x) = {x}^{4} + {x}^{3} - 2 {x}^{2} + x + 1$

$p(1) = {(1)}^{4} + {(1)}^{3} - 2 {(1)}^{2} + (1) + 1$

or

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

or

$\bf p(1) = 2$

Thus,

Remainder is 2, when x⁴+ x³-2x²+ x + 1 is divided by x-1.

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