Question

F(x) = x^3 + 6x^2 + x1/2 and g(x)= x^1/2. Find f(x) ÷ g(x)

A) x^5/2 + 6x^3/2-1
B) (x^5+6x^3 +1)1/2
C) x5/2 +6x^3/2 + 1
D) x^3/2 + 6x+ x1/4
E) x3/2 - 6x + x1/4

Answer 1

`(f(x))/(g(x))=x^{(5)/(2)} +6 x^{(3)/(2)} +1}`

Explanation:

`f(x)=x^3+6x^2+√(x)`

`g(x)= √(x)`

we are asked to determine

`(f(x))/(g(x))`

Let us do it step by step.

`f(x)=x^3+6x^2+√(x)`

`f(x)=x^2 * x+6x * x +√(x)`

`f(x)=x^2 * √(x) * √(x) +6x * √(x) * √(x) +√(x)`

Taking
`√(x)` as GCF

`f(x)= √(x)(x^2 * √(x) +6x * √(x) +1)`

Hence

`(f(x))/(g(x))=(√(x)(x^2 * √(x) +6x * √(x) +1))/( √(x))`

`(f(x))/(g(x))=x^2 * √(x) +6x * √(x) +1`

`√(x)=x^(1)/(2)`

`(f(x))/(g(x))=x^2 * x^{(1)/(2)} +6 * x * x^{(1)/(2)} +1`

Using law of exponents

`a^m * a^n = a^(m+n)`

`(f(x))/(g(x))=x^{2+(1)/(2)} +6 * x^{1+(1)/(2)} +1}`

`(f(x))/(g(x))=x^{(5)/(2)} +6 x^{(3)/(2)} +1}`