Question

Determine if the following expressions are equivalent? Justify your answer.

6x^2+7x-3
f(x)=_____________ and g(x)=3x(3x-1)-(1+9x^2)
2x+3

Answer 1

i solved it numerically already, with a 2. it gives me the same answer, 5.

Answer 2

\[ \large g(x)=3x(3x-1)-(1+9x^2)=9x^2-3x-1-9x^2=-(3x+1) \]

Answer 3

i got that i just didnt know what to do with it

Answer 4

using synthetic division for \(f(x)\):
\[ \large \begin{array}{r|rrr}
& 6 & 7 & -3\\
-3/2 & & -9 & 3\\ \hline
& 6 & -2 & 0
\end{array} \]
so
\[ \large f(x)=\frac{(x+3/2)(6x-2)}{2x+3}=
\frac{1/2(2x+3)(6x-2)}{2x+3}= \]
\[ \large =\frac{1/2(6x-2)}{1}=3x-1 \]

Answer 5

so \(f(x)=3x-1\) and \(g(x)=-3x-1\).
\(f\equiv g\)??

Answer 6

you confused me at the synthetic division part.

Answer 7

thats not wat im learning right now.