91Ó°ÊÓ

Writing Briefly explain how to check polynomial division, and justify your reasoning. Give an example.

(a) use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. (b) Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. $$f(x)=0.11 x^{3}-2.07 x^{2}+9.81 x-6.88$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$f(x)=3 x^{3}+2 x^{2}+x+3$$

Assume that the function $$f(x)=a x^{2}+b x+c, a \neq 0$$ has two real zeros. Prove that the \(x\) -coordinate of the vertex of the graph is the average of the zeros of \(f\).

(a) use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. (b) Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. $$g(x)=3 x^{4}+4 x^{3}-3$$

Determine whether the statement is true or false. Justify your answer. $$i^{44}+i^{150}-i^{74}-i^{109}+i^{61}=-1$$

Find the constant \(c\) such that the denominator will divide evenly into the numerator. $$\frac{x^{3}+4 x^{2}-3 x+c}{x-5}$$

Use synthetic division to verify the upper and lower bounds of the real zeros of \(f\) \(f(x)=x^{3}+3 x^{2}-2 x+1\) (a) Upper: \(x=1\) (b) Lower: \(x=-4\)

(a) use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. (b) Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. $$h(x)=x^{4}-10 x^{2}+3$$

Use synthetic division to verify the upper and lower bounds of the real zeros of \(f\) \(f(x)=x^{3}-4 x^{2}+1\) (a) Upper: \(x=4\) (b) Lower: \(x=-1\)