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