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) ---
Polynomials, EXT1 EQ-Bank 7
Consider a polynomial \(y=(x+3)^2(2-x) \cdot Q(x)\)
where \(Q(x)=6-x-x^2\)
Explain what happens to \(y\) as \(x \rightarrow-\infty\). (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
Polynomials, EXT1 EQ-Bank 3
Consider the polynomial \(P(x)=x(3-x)^3\).
- State the degree of the polynomial and identify the leading coefficient. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Explain what happens to \(y\) as \(x \rightarrow \pm \infty\). (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Without using calculus, sketch \(P(x)\) showing its general form and any \(x\)-intercepts. (2 marks)
--- 6 WORK AREA LINES (style=lined) ---
Show Answers Only
a. \(\text{Degree}\ P(x)=4\)
\(\text{Leading co-efficient}=-1\)
b. \(\text{As} \ \ x \rightarrow-\infty,-x^4 \rightarrow-\infty, \ y \rightarrow-\infty\).
\(\text{As} \ \ x \rightarrow \infty,-x^4 \rightarrow-\infty, \ y \rightarrow-\infty\).
c. \(P(x)\ \text{has zeroes at}\ \ x=0, 3:\)
Show Worked Solution
a. \(\text{Degree}\ P(x)=4\)
\(\text{Leading co-efficient}=-1\)
b. \(\text{As} \ \ x \rightarrow-\infty,-x^4 \rightarrow-\infty, \ y \rightarrow-\infty\).
\(\text{As} \ \ x \rightarrow \infty,-x^4 \rightarrow-\infty, \ y \rightarrow-\infty\).
c. \(P(x)\ \text{has zeroes at}\ \ x=0, 3:\)
Polynomials, EXT1 EQ-Bank 2
Consider a polynomial \(y=-2 x^5-26 x^4-x+1\).
With reference to the leading term, explain what happens to \(y\) as \(x \rightarrow-\infty\). (2 marks)
--- 5 WORK AREA LINES (style=lined) ---