Q5.

Question

State the degree and leading coefficient of polynomial $5 x^{6} - 8 x^{2}$ in one variable. If it is not a polynomial in one variable, explain why.

Step-by-Step Solution

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Answer

The polynomial has degree $6$ and leading coefficient $5$ .

1Step 1. Write down the given information.

The given polynomial is $5 x^{6} - 8 x^{2}$ .

2Step 2. Calculation.

The degree and leading coefficient of the given polynomial $5 x^{6} - 8 x^{2}$ are stated as:

The given polynomial is a polynomial in one variable. Therefore, by concept of degree and leading coefficient of a polynomial, the degree of the polynomial is $6$ and leading coefficient is $5$ .

3Step 3. Conclusion.

The polynomial has degree $6$ and leading coefficient $5$ .

Q4.

Q6.

Other exercises in this chapter

Q3.

OPEN ENDED Sketch the graph of an odd-degree polynomial function with a negative leading coefficient and three real roots.

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Q4.

Tell whether the following statement is always, sometimes or never true. Explain. A polynomial function that has four real roots is a fourth-degree polynomial.

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Q6.

State the degree and leading coefficient of polynomial 2b+4b3-3b5-7 in one variable. If it is not a polynomial in one variable, explain why.

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Q7.

Find p3 and p-1 for the function px=-x3+x2-x.

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