Evaluating Polynomials and Exponents

The video tutorial explains how to evaluate polynomials by substituting given values for variables. It covers two examples: one with a cubic polynomial and another with a polynomial involving fractions. The process involves substituting the variable, simplifying exponents, performing multiplication, and adding results. The tutorial emphasizes the order of operations and provides a detailed walkthrough of each step, ensuring clarity in solving polynomial expressions.

What is the first step in evaluating a polynomial for a given variable value?

• Simplify the exponents

• Substitute the variable with its value

• Multiply all terms

• Add all coefficients

After substituting x = -2 in the polynomial 4x^3 - 5x + 7, what is the expression?

• 4(-2)^3 - 5(-2) - 7

• 4(-2)^3 - 5(-2) + 7

• 4(-2)^3 + 5(-2) + 7

• 4(-2)^2 - 5(-2) + 7

What is the result of simplifying the expression 4(-2)^3?

• 32

• -32

• -8

• 8

What is the final result of evaluating the polynomial 4x^3 - 5x + 7 for x = -2?

• -22

• 15

• -15

• 22

When substituting y = 4 in the polynomial -3/4y^4 + 2y^2, what is the expression?

• -3/4(4)^3 + 2(4)^2

• -3/4(4)^2 + 2(4)^2

• -3/4(4)^4 - 2(4)^2

• -3/4(4)^4 + 2(4)^2

What is the value of 4 raised to the fourth power?

• 512

• 256

• 128

• 64

How can you simplify the multiplication of -3/4 and 256?

• By dividing 256 by 4 first

• By multiplying directly

• By adding 256 and 4

• By subtracting 4 from 256

What is the result of multiplying -3 by 64?

• -192

• 64

• 192

• -64

What is the final result of evaluating the polynomial -3/4y^4 + 2y^2 for y = 4?

• 128

• -160

• 160

• -128

What is the common factor between 4 and 256 that can be used to simplify the expression?

• 2

• 16

• 4

• 8