Question

divide thepolynomial p(x) by the polynomial g(x) and find the quotient and reainder

p(x)=x4-3x2+4x+5, g(x)=x2+1-x

Answer 1

Given p(x) = x^4 - 3x^2 + 4x + 5 - > Dividend

Given g(x) = x^2 + 1 - x - > Divisor

Remainder = 8

Quotient = x^2 + x - 3

Now,

We know that Dividend = Divisor * Quotient + Remainder.

= > (x^2 + 1 - x) * (x^2 + x - 3) + 8

= > (x^4 + x^3 - 3x^2 + x^2 + x - 3 - x^3 - x^2 + 3x) + 8

= > x^4 - 3x^2 + 4x - 3 + 8

= > x^4 - 3x^2 + 4x + 5.

= > Dividend.

Hope this helps!

Answer 2

hello,

Solution:

x² -x +1 ) x4 - 3x²+4x+5 (x² +x -3

x4 + x² -x³

- - +

________________________

x³ - 4x² +4x +5

x³ -x² + x

- + -

_______________

-3x² +3x +5

- 3x² +3x -3

+ - +

______________________

8

______________________

So, Quotient polynomial is (x² +x -3)

Remainder is 8.

hope it helps you.