Polynomial Degree and Leading Coefficients

This video tutorial explains how to write polynomials in standard form, identify the degree and leading coefficient, and handle polynomials with multiple variables. It covers several examples, including simple, constant, and multi-variable polynomials, and introduces the concept of the zero polynomial.

What is the first step in writing a polynomial in standard form?

• Add all coefficients.

• Arrange terms alphabetically.

• Identify the smallest power.

• Find the largest power.

In the polynomial 4x^2 - 5x^7 - 2 + 3x, which term should be written first?

• 4x^2

• -5x^7

• 3x

• -2

What is the degree of the polynomial 4x^2 - 5x^7 - 2 + 3x?

• 7

• 4

• 3

• 2

What is the leading coefficient of the polynomial 4x^2 - 5x^7 - 2 + 3x?

• 4

• -5

• 3

• -2

In the polynomial 4 - 9x^2, which term is written first in standard form?

• 4

• -9x^2

• x^2

• -4

What is the degree of the polynomial 4 - 9x^2?

• 2

• 0

• 3

• 1

What is the leading coefficient of the polynomial 4 - 9x^2?

• 4

• -9

• 0

• 9

What is the degree of the constant polynomial 8?

• 8

• 0

• Undefined

• 1

What is the leading coefficient of the constant polynomial 8?

• 0

• 1

• 8

• Undefined

In the polynomial x^4 - 4 + x, what is the degree?

• 1

• 2

• 3

• 4