Using the remainder theorem and checking your answer with synthetic division

The video tutorial covers the remainder theorem, explaining how to determine the remainder of a polynomial when a specific value is substituted for the variable. It demonstrates the application of the theorem with an example, showing the calculation process. The tutorial also introduces the factor theorem, explaining its relation to the remainder theorem. Additionally, synthetic division is explained as an alternative method for verifying results. The video concludes by summarizing the key points and emphasizing the importance of understanding these concepts for solving polynomial equations.

What does the remainder theorem help you determine when dividing a polynomial by a linear divisor?

• The constant term of the polynomial

• The leading coefficient of the polynomial

• The remainder of the division

• The degree of the polynomial

In the example provided, what is the remainder when the polynomial is evaluated at x = 4?

• 0

• 11

• 28

• 39

Which method can be used as an alternative to the remainder theorem to verify the remainder?

• Completing the square

• Synthetic division

• Long division

• Partial fraction decomposition

What is a key difference between the remainder theorem and synthetic division?

• The remainder theorem provides the remainder, while synthetic division can also identify factors

• Synthetic division is only applicable to polynomials with real coefficients

• The remainder theorem is more accurate than synthetic division

• Synthetic division can only be used for quadratic polynomials

When using synthetic division, what does a remainder of zero indicate?

• The polynomial has no real roots

• The divisor is a factor and a zero of the polynomial

• The divisor is not a factor

• The polynomial is irreducible