91Ó°ÊÓ

Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.\((-6,744),(-4,154),(-2,4),(0,-6),(2,16)\) \((4,154),(6,684),(8,2074),(10,4984)\)

In Exercises 11–18, divide using synthetic division. $$ \left(x^2+8 x+1\right) \div(x-4) $$

Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.\((1,0),(2,6),(3,2),(4,6),(5,12),(6,-10)\) \((7,-114),(8,-378),(9,-904)\)

Write three different cubic functions that pass through the points \((3,0),(4,0)\), and \((2,6)\). Justify your answers.

MODELING WITH MATHEMATICS During a recent period of time, the numbers (in thousands) of males \(M\) and females \(F\) that attend degree-granting institutions in the United States can be modeled by $$ \begin{aligned} &M=19.7 t^2+310.5 t+7539.6 \\ &F=28 t^2+368 t+10127.8 \end{aligned} $$ where \(t\) is time in years. Write a polynomial to model the total number of people attending degree- granting institutions. Interpret its constant term.

Factor the polynomial completely. $$ g^3-343 $$

Find the zeros of the function. Then sketch a graph of the function. \(g(x)=-4 x^4+8 x^3+60 x^2\)

Describe and correct the error in factoring the polynomial. $$ \begin{aligned} 3 x^3+27 x &=3 x\left(x^2+9\right) \\ &=3 x(x+3)(x-3) \end{aligned} $$

According to the Rational Root Theorem, which is not a possible zero of the function \(f(x)=40 x^5-42 x^4-107 x^3+107 x^2+33 x-36 ?\) (A) \(-\frac{2}{3}\) (B) \(-\frac{3}{8}\) (C) \(\frac{3}{4}\) (D) \(\frac{4}{5}\)

\(f(x)=x^3-6\); translation 3 units left, followed by a reflection in the \(y\)-axis