Evaluating Polynomials and Functions

This video tutorial teaches how to evaluate polynomials for given values using substitution. It begins with an introduction to polynomial evaluation and a review of the order of operations. The tutorial provides examples of evaluating polynomials for specific values of x, including both positive and negative numbers. It also covers evaluating polynomials in function notation and concludes by answering the original question posed at the beginning. The lesson emphasizes the importance of using parentheses and following the correct order of operations to avoid common mistakes.

What is the first step in evaluating a polynomial using substitution?

• Multiplying coefficients

• Replacing variables with given values

• Adding constants

• Simplifying exponents

In the order of operations, which step comes first?

• Simplifying parentheses

• Subtraction

• Addition

• Multiplication

What is the result of 21 minus 2 times 7 minus 4 squared plus 13?

• 16

• 18

• 22

• 20

When substituting a number for a variable, what common mistake should be avoided?

• Forgetting to add

• Not using parentheses

• Skipping multiplication

• Ignoring exponents

What is the value of 4x cubed minus 6x squared plus 2x minus 5 for x equals 3?

• 60

• 50

• 55

• 45

How does the value of x being negative affect the evaluation of a polynomial?

• It only affects the constants

• It changes the sign of the result

• It makes no difference

• It only affects the exponents

What is the result of evaluating 4x cubed minus 6x squared plus 2x minus 5 for x equals negative 3?

• -150

• -160

• -173

• -180

In function notation, what does f(4) equal for f(x) = 3x squared minus 2?

• 48

• 46

• 44

• 50

What is the value of f(-1) for f(x) = 3x squared minus 2?

• 0

• 3

• 1

• 2

What is the final result of x squared plus 2x minus 7 when x equals 3?

• 6

• 9

• 7

• 8