Factor Theorem and Polynomial Division

The video tutorial explains the factor theorem and its connection to the remainder theorem. It demonstrates how to factor a polynomial using these theorems and discusses the use of long and synthetic division. The tutorial provides a step-by-step example of applying the factor theorem to determine zeros and factors, followed by a verification process using calculations.

What is the primary focus of the Factor Theorem?

• Checking if a polynomial is divisible by a binomial

• Determining the degree of a polynomial

• Finding the roots of a polynomial

• Calculating the derivative of a polynomial

How is the Factor Theorem related to the Remainder Theorem?

• Both are used to find the roots of a polynomial

• Both are used to determine divisibility of polynomials

• Both involve calculating the derivative of a polynomial

• Both are used to find the degree of a polynomial

What is one method mentioned for factoring a polynomial?

• Completing the square

• Long division

• Integration

• Differentiation

Which division method is suggested as an alternative to long division?

• Matrix division

• Polynomial expansion

• Partial fraction decomposition

• Synthetic division

What does it mean if x + 1 is a factor of a polynomial?

• The polynomial is a constant

• The polynomial has a degree of 1

• The polynomial equals zero when x = 1

• The polynomial equals zero when x = -1

What value of x is tested to check if x + 1 is a factor?

• x = 0

• x = 1

• x = -1

• x = 2

What result indicates that x + 1 is a factor of the polynomial?

• The polynomial equals -1

• The polynomial equals 5

• The polynomial equals 1

• The polynomial equals 0

What is the first step in verifying the Factor Theorem?

• Graphing the polynomial

• Dividing the polynomial by x + 1

• Substituting x = -1 into the polynomial

• Finding the derivative of the polynomial

What is the result of substituting x = -1 into the polynomial?

• The result is 5

• The result is -5

• The result is 0

• The result is 1

What conclusion is drawn if the result of substitution is not zero?

• The polynomial is quadratic

• x + 1 is not a factor

• x + 1 is a factor

• The polynomial is linear