Answer :
Polynomials are q(x) = 6x² - x and r(x) = 90x⁴ + 39x³ + 3 so that f(x)=q(x)g(x)+r(x).
Let's perform the polynomial long division to divide f(x) by g(x):
Given:
f(x) = (6x² - x) . g(x) + (90x⁴ + 39x³ + 3)
g(x) = -10x² - x + 15
We'll perform the division f(x)/g(x). Here's how it's done:
6x - 1
________________________________________________________
-10x² - x + 15 | 90x⁴ + 39x³ + 3
-(90x⁴ + 9x³ - 135x²)
___________________________
30x³ + 135x² + 3
-(30x³ + 3x² - 45x)
__________________
138x
-(138x - 13.8)
___________
13.8
So, after performing the division, we get:
q(x) = 6x - 1
r(x) = 90x⁴ + 39x³ + 3
Therefore, q(x) = 6x² - x and r(x) = 90x⁴ + 39x³ + 3.
Complete question is:
Take f and g to be the polynomials that are given by f(x)=70x⁴-3x³-196x²+9x+124 and g(x)=-10x²-x+15. Identify polynomials q and r so that f(x)=q(x)g(x)+r(x). q(x)=|6x²-x || r(x)=
