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Magazine Problem 13
A polynomial \(P\) is given. (a) Find all zeros of \(P\), real and complex. (b) Factor \(P\) completely. $$P(x)=x^{3}+8$$
Problem 13
Find the \(x\) - and \(y\) -intercepts of the rational function. $$t(x)=\frac{x^{2}-x-2}{x-6}$$
Problem 14
Find the \(x\) - and \(y\) -intercepts of the rational function. $$r(x)=\frac{2}{x^{2}+3 x-4}$$
Problem 14
A polynomial \(P\) is given. (a) Find all zeros of \(P\), real and complex. (b) Factor \(P\) completely. $$P(x)=x^{3}-8$$
Problem 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 $$\frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$$ $$P(x)=x^{5}+x^{4}-2 x^{3}+x+1, \quad D(x)=x^{2}+x-1$$
Problem 14
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. $$f(x)=x^{2}-2 x+2$$
Problem 15
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. $$f(x)=-x^{2}+6 x+4$$
Problem 15
Evaluate the expression and write the result in the form \(a+b i\) $$(2-5 i)+(3+4 i)$$
Problem 15
Find the \(x\) - and \(y\) -intercepts of the rational function. $$r(x)=\frac{x^{2}-9}{x^{2}}$$
Problem 15
Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. (GRAPH CANT COPY) $$P(x)=(x-1)(x+2)$$
