To determine the value of the quotient of a polynomial function:
[tex]\frac{3x^2-27x}{2x^2+13x-7}\text{ x }\frac{4x^2-1}{3x}[/tex]
The quotient consists of the numerator which represents the first box
while the denominator represents the second box
[tex]\begin{gathered} \frac{3x^2-27x}{2x^2+13x-7}\text{ x}\frac{4x^2-1}{3x} \\ \frac{3x(x-9)}{2x^2+14x-x-7}\text{ x}\frac{(2x)^2-1}{3x} \\ \frac{3x(x-9)}{2x(x_{}+7)-1(x+7)}\text{ x }\frac{(2x-1)(2x+1)}{3x} \\ \frac{3x(x-9)(2x-1)(2x+1)}{(2x-1)(x+7)3x} \end{gathered}[/tex][tex]\frac{(x-9)(2x+1)}{(x+7)}[/tex]
Therefore the simplest form of the quotient has a numerator of (x-9)(2x+1) and a denominator of (x+7)
The expression does exist when x = 0
