Polynomials, EXT1 EQ-Bank 12

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)

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\(\text{As}\ \ x \rightarrow-\infty,\ \ x^{5}\ \rightarrow-\infty\)

\(\text{Since the leading coefficient \((-2)\) is negative:}\)

\(\text{As}\ \ x \rightarrow-\infty,\ \ y \rightarrow \infty.\)

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\(\text{As}\ \ x \rightarrow-\infty,\ \ x^{5}\ \rightarrow-\infty\)

\(\text{Since the leading coefficient \((-2)\) is negative:}\)

\(\text{As}\ \ x \rightarrow-\infty,\ \ y \rightarrow \infty.\)