divide the polynomials. your answer should be in the form $p(x)+\frac{k}{x - 1}$ where $p$ is a polynomial…

divide the polynomials. your answer should be in the form $p(x)+\frac{k}{x - 1}$ where $p$ is a polynomial and $k$ is an integer. $\frac{x^{2}+6x - 4}{x - 1}=$

divide the polynomials. your answer should be in the form $p(x)+\frac{k}{x - 1}$ where $p$ is a polynomial and $k$ is an integer. $\frac{x^{2}+6x - 4}{x - 1}=$

Answer

Explanation:

Step1: Use polynomial long - division

We divide $x^{2}+6x - 4$ by $x - 1$. First, divide the leading term of the dividend $x^{2}+6x - 4$ (which is $x^{2}$) by the leading term of the divisor $x - 1$ (which is $x$). $\frac{x^{2}}{x}=x$.

Step2: Multiply and subtract

Multiply $x - 1$ by $x$ to get $x^{2}-x$. Subtract this from the dividend: $(x^{2}+6x - 4)-(x^{2}-x)=x^{2}+6x - 4 - x^{2}+x = 7x-4$.

Step3: Repeat the process

Divide the leading term of the new dividend $7x-4$ (which is $7x$) by the leading term of the divisor $x$ (from $x - 1$). $\frac{7x}{x}=7$.

Step4: Multiply and find the remainder

Multiply $x - 1$ by $7$ to get $7x-7$. Subtract this from the new dividend: $(7x - 4)-(7x - 7)=7x - 4-7x + 7=3$.

Answer:

$x + 7+\frac{3}{x - 1}$