Chapter 7: Q20. (page 350)

State the degree and leading coefficient of polynomial $7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$ in one variable. If it is not a polynomial in one variable, explain why.

Short Answer

Expert verified

The polynomial has degree $3$ and leading coefficient $- 5$ .

Step by step solution

Step 1. Write down the given information.

The given polynomial is $7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$ .

Step 2. Calculation.

Re-arranging the given polynomial $7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$ in descending order of degree, the polynomial can be written as $- 5 x^{3} + 9 x^{2} - 2 x + 7$ .

Now, the degree and leading coefficient of the polynomial $- 5 x^{3} + 9 x^{2} - 2 x + 7$ are stated as:

The polynomial $- 5 x^{3} + 9 x^{2} - 2 x + 7$ is a polynomial in one variable $(x)$ . Therefore, by concept of degree and leading coefficient of a polynomial, the degree of the polynomial is $3$ and leading coefficient is $- 5$ .

Step 3. Conclusion.

The polynomial has degree 3 and leading coefficient $- 5$ .

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State the degree and leading coefficient of polynomial $7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$ in one variable. If it is not a polynomial in one variable, explain why.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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State the degree and leading coefficient of polynomial 7+3x2-5x3+6x2-2x in one variable. If it is not a polynomial in one variable, explain why.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

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Study anywhere. Anytime. Across all devices.

State the degree and leading coefficient of polynomial $7 + 3 x^{2} - 5 x^{3} + 6 x^{2} - 2 x$ in one variable. If it is not a polynomial in one variable, explain why.