Divide the polynomals. Your answer should be in the form p(x)+(k)/(x+3) where p is a polynomial and kis an integer. (x^2-7)/(x+3)=square

To divide the polynomial $\frac{x^2 - 7}{x + 3}$, we can use polynomial long division.<br /><br />Step 1: Divide the first term of the numerator by the denominator.<br />$\frac{x^2}{x + 3} = x$<br /><br />Step 2: Multiply the denominator by the result from step 1 and subtract it from the numerator.<br />$(x + 3) \cdot x = x^2 + 3x$<br />$x^2 - 7 - (x^2 + 3x) = -3x - 7$<br /><br />Step 3: Repeat the process with the new numerator.<br />$\frac{-3x}{x + 3} = -3$<br /><br />Step 4: Multiply the denominator by the result from step 3 and subtract it from the new numerator.<br />$(-3)(x + 3) = -3x - 9$<br />$-3x - 7 - (-3x - 9) = 2$<br /><br />So, the final answer is:<br />$\frac{x^2 - 7}{x + 3} = x - 3 + \frac{2}{x + 3}$<br /><br />Therefore, the polynomial division of $\frac{x^2 - 7}{x + 3}$ is $x - 3 + \frac{2}{x + 3}$.