Question

What is the value of the remainder if 10x4 – 6x3 + 5x2 – x + 1 is divided by x – 3?

Answer 1

The remainder = 691

Explanation:

Let p(x) = 10x⁴ - 6x³ + 5x² - x + 1

We have to divide p(x) by (x - 3)

To find the remainder we have to find p(3)

To find the remainder

p(x) = 10x⁴ - 6x³ + 5x² - x + 1

p(3) = 10 * (3)⁴ - 6*(3)³ + 5* (3)² - 3 + 1

= (10 * 81 ) - ( 6 * 27 ) + (5 * 9) - 3 + 1

= 810 - 162 + 45 - 3 + 1 = 691

Therefore the remainder is 691

Answer 2

Remainder is 691.

Explanation:

Given function is
`10x^4-6x^3+5x^2-x+1`.

Now we need to find remainder if we divide given function
`10x^4-6x^3+5x^2-x+1` by (x-3)

(x-3) means plug x=3 into
`10x^4-6x^3+5x^2-x+1` to find remainder.

`10x^4-6x^3+5x^2-x+1`

`=10(3)^4-6(3)^3+5(3)^2-(3)+1`

`=10(81)-6(27)+5(9)-(3)+1`

`=810-162+45-3+1`

`=856-162-3`

`=856-165`

`=691`

Hence remainder is 691.