Question

@ash2326 5.Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x – 5. Find

Answer 1

Just 5 minutes

Answer 2

ok :)

Answer 3

Sorry taking me long. I'll be on it ASAP

Answer 4

dont worry about it take your time :)

Answer 5

Hey ricky

Answer 6

yes?

Answer 7

ash i will get back online in 20 minutes i have to go for a little bit :/

Answer 8

We have
\[f(x)=x^4-8x^3+16x^2-19\]
and
\[g(x)=x-5\]
We want to find \[\frac{f(x)}{g(x)}\]
Let's divide


__x^3____________________________________
x-5 | x^4-8x^3+16x^2-19
x^4-5x^3

__x^3___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3

__x^3___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19

__x^3-3x^2___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-3x^3+15x^2

__x^3-3x^2___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)


__x^3-3x^2___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)
x^2-19



__x^3-3x^2+x___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)
x^2-19
-( x^2-5x)


__x^3-3x^2+x___________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)
x^2-19
-(x^2-5x)
5x-19


__x^3-3x^2+x_+5_________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)
x^2-19
-(x^2-5x)
5x-19
(5x-25)

__x^3-3x^2+x+5_________________________________
x-5 | x^4-8x^3+16x^2-19
-( x^4-5x^3)
0 -3x^3+16x^2-19
-( -3x^3+15x^2)
x^2-19
-(x^2-5x)
5x-19
- (5x-25)
6
so we get quotient \[x^3-3x^2+x+5\]
and remainder 6