91Ó°ÊÓ

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its x- and y-intercept(s). (c) Sketch its graph. $$ f(x)=-x^{2}+10 x $$

Find the \(x\) -and \(y\) -intercepts of the rational function. $$ s(x)=\frac{3 x}{x-5} $$

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

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

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

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its x- and y-intercept(s). (c) Sketch its graph. $$ f(x)=x^{2}+4 x+3 $$

\(9-14\) . 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 $$ \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)} $$ $$ P(x)=2 x^{4}-x^{3}+9 x^{2}, \quad D(x)=x^{2}+4 $$

\(9-14\) . 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 $$ \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)} $$ $$ P(x)=x^{5}+x^{4}-2 x^{3}+x+1, \quad D(x)=x^{2}+x-1 $$

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. \(P(x)=x^{3}-8\)