Understanding Opposites in Algebraic Expressions

The video tutorial explains how to find the opposite of a polynomial expression by multiplying it by negative one. It begins with a general explanation of what 'opposite' means in mathematical terms, using simple number examples. The tutorial then applies this concept to a polynomial, demonstrating the process of distributing negative one across each term of the expression to find its opposite.

What is the first step in finding the opposite of a polynomial expression?

• Add 1 to each term

• Subtract 1 from each term

• Multiply the entire expression by negative one

• Divide each term by 2

If the opposite of 5 is -5, what is the opposite of -8?

• -8

• 0

• 8

• -16

What operation is used to find the opposite of a number?

• Division

• Multiplication by negative one

• Subtraction

• Addition

To find the opposite of the polynomial 2x^2 - 7x + 13, what should you do?

• Divide each term by negative one

• Multiply the entire polynomial by negative one

• Add 1 to each term

• Multiply each term by 2

What is the result of multiplying -1 by 2x^2?

• 0

• -2x^2

• x^2

• 2x^2

What happens when you multiply -1 by -7x?

• -7x

• -14x

• 7x

• 0

What is the result of multiplying -1 by 13?

• 13

• 26

• 0

• -13

What is the opposite of the polynomial 2x^2 - 7x + 13?

• 2x^2 - 7x - 13

• -2x^2 - 7x + 13

• -2x^2 + 7x - 13

• 2x^2 + 7x + 13

Which of the following is NOT a step in finding the opposite of a polynomial?

• Changing the sign of each term

• Multiplying each term by negative one

• Distributing negative one across the polynomial

• Adding negative one to each term

What is the final expression after finding the opposite of 2x^2 - 7x + 13?

• -2x^2 - 7x - 13

• 2x^2 - 7x + 13

• 2x^2 + 7x - 13

• -2x^2 + 7x - 13