Synthetic Substitution and Remainder Theorem

The video tutorial from MooMooMath introduces synthetic substitution, also known as the remainder theorem, as a method to evaluate polynomials. It explains how to substitute values into a polynomial using function notation and synthetic division. The tutorial provides a step-by-step guide on performing synthetic division, highlighting the importance of the remainder in determining the output of a function. An example problem is solved to demonstrate the process, and the video concludes with a summary of the key points discussed.

What is another name for synthetic substitution?

• Division theorem

• Polynomial theorem

• Remainder theorem

• Factor theorem

In synthetic substitution, what do you substitute into the polynomial?

• The variable y

• The constant term

• A specific value for x

• The coefficient of x

What is the first step in synthetic substitution?

• Multiply the coefficients

• Bring down the leading coefficient

• Subtract the remainder

• Add the constant term

What does the remainder in synthetic substitution represent?

• The output of the function for the substituted value

• The degree of the polynomial

• The product of the roots

• The sum of all coefficients

How do you write the result of synthetic substitution in function notation?

• f(x) = x^2 + 27

• f(x) = 2x + 27

• f(2) = 27

• f(x) = remainder

What is the result of evaluating the polynomial 2^4 + 2^2 - 2 + 5?

• 24

• 22

• 27

• 25

Which method can be used to verify the result of synthetic substitution?

• Graphical method

• Direct evaluation

• Factoring

• Completing the square

What is the final output when using synthetic substitution for the value 2 in the given example?

• 32

• 27

• 22

• 12