91Ó°ÊÓ

Find the \(x\)- and \(y\)-intercepts of the rational function. $$t(x)=\frac{x^{2}-x-2}{x-6}$$

Two polynomials \(P\) and \(D\) are given. Use either synthetic or long division to divide \(P(x)\) by \(D(x),\) and express the quotient \(P(x)/D(x)\) in the form $$\frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$$. $$P(x)=x^{2}+4 x-8, \quad D(x)=x+3$$

Two polynomials \(P\) and \(D\) are given. Use either synthetic or long division to divide \(P(x)\) by \(D(x),\) and express the quotient \(P(x)/D(x)\) in the form $$\frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$$. $$P(x)=x^{3}+6 x+5, \quad D(x)=x-4$$

Find the \(x\)- and \(y\)-intercepts of the rational function. $$r(x)=\frac{2}{x^{2}+3 x-4}$$

A polynomial \(P\) is given. (a) Find all zeros of \(P,\) real and complex. (b) Factor \(P\) completely. $$P(x)=x^{4}+6 x^{2}+9$$

Find the real and imaginary parts of the complex number. $$i \sqrt{3}$$

Find the real and imaginary parts of the complex number. $$\sqrt{3}+\sqrt{-4}$$

Find the \(x\)- and \(y\)-intercepts of the rational function. $$r(x)=\frac{x^{2}-9}{x^{2}}$$

A polynomial \(P\) is given. (a) Find all zeros of \(P,\) real and complex. (b) Factor \(P\) completely. $$P(x)=x^{3}+8$$

Two polynomials \(P\) and \(D\) are given. Use either synthetic or long division to divide \(P(x)\) by \(D(x),\) and express the quotient \(P(x)/D(x)\) in the form $$\frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$$. $$P(x)=4 x^{2}-3 x-7, \quad D(x)=2 x-1$$