Polynomials, EXT1 EQ-Bank 11 A polynomial \(f(x)\) is defined by \(f(x)=-3x^3+27x^2+12x-1\) Explain what happens to \(f(x)\) as \(x \rightarrow-\infty\). (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only \(\text{Since}\ f(x) \ \text{has degree 3:}\) \(\text{As} \ \ x \rightarrow-\infty, x^3 \rightarrow-\infty\) \(f(x) \ \text{has leading coefficient}=-3\) \(\therefore\ \text{As} \ \ x \rightarrow-\infty,-3 x^3 \rightarrow \infty, \ f(x) \rightarrow \infty\) Show Worked Solution \(\text{Since}\ f(x) \ \text{has degree 3:}\) \(\text{As} \ \ x \rightarrow-\infty, x^3 \rightarrow-\infty\) \(f(x) \ \text{has leading coefficient}=-3\) \(\therefore\ \text{As} \ \ x \rightarrow-\infty,-3 x^3 \rightarrow \infty, \ f(x) \rightarrow \infty\)