You can either use the process of long division or synthetic division for this problem

Both ways you get the same answer:

x^3 3x^2 9x 27

Remainder: 88

Factor out (x 3) in all but the 88 term:

x^4 7 = (x 3)(x^3 3x^2 9x 27) 88

x^4 7 = x^4 7 x^3(x 3) x^3(x 3)

= x^4 7 x^3(x 3) x^4 3x^3

= x^3(x 3) 3x^3 7

Factor out (x 3) in all but the 88 term:

x^4 7 = (x 3)(x^3 3x^2 9x 27) 88

= x^3(x 3) 3x^3 7 3x^2(x 3) (3x^3 9x^2)

= x^3(x 3) 3x^2(x 3) 9x^2 7

Again to reduce 9x^2 7:

= x^3(x 3) 3x^2(x 3) 9x^2 7 9x(x 3) (9x^2 27x)

= x^3(x 3) 3x^2(x 3) 9x(x 3) 27x 7

And finally write 27x 7 as 27(x 3) 88;

x^4 7 = x^3(x 3) 3x^2(x 3) 9x(x 3) 27(x 3) 88

Factor out (x 3) in all but the 88 term:

x^4 7 = (x 3)(x^3 3x^2 9x 27) 88

That means that:

(x^4 7) / (x 3) = x^3 3x^2 9x 27 with a remainder of 88

You can either use the process of long division or synthetic division for this problem

Both ways you get the same answer:

x^3 3x^2 9x 27

Remainder: 88

That makes r(x) = 3x^3 7. Do the same thing to reduce r(x) by adding/subtracting 3x^2(x 3) = 3x^3 9x^2:

http://www.wolframalpha.com/input/i=(x^4+7)

This post is last updated on hrtanswers.com at Date : 1st of September – 2022