Question

which of the following is a 5th degree polynomial with a leading coefficient of 1 and a constant term of negative 6? (hint: if there is no coefficient in front of a variable, that means the coefficient is actually 1.)
$x^{5}-3x^{2}+2x - 5$
$x^{5}-3x^{2}+2x - 6$
$x^{4}-3x^{2}+2x - 6$
$x^{5}-3x^{2}+2x + 6$
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Explanation:

Step1: Check degree

A 5th - degree polynomial has the highest power of the variable \(x\) equal to 5. So we can eliminate \(x^{4}-3x^{2}+2x - 6\) (degree 4).

Step2: Check leading coefficient

The leading term of a polynomial \(a_nx^n+a_{n - 1}x^{n-1}+\cdots+a_1x + a_0\) is \(a_nx^n\) and \(a_n\) is the leading coefficient.
For \(x^{5}-3x^{2}+2x-5\), the leading coefficient is \(1\).
For \(x^{5}-3x^{2}+2x + 6\), the leading coefficient is \(1\).
For \(x^{5}-3x^{2}+2x-6\), the leading coefficient is \(1\). But we need a leading coefficient of \(1\), a constant term of \(- 6\) (since if there is no coefficient in front of a variable, the coefficient is actually \(1\)).

Answer:

\(x^{5}-3x^{2}+2x-6\)