Adding Polynomials: Horizontal vs Vertical Methods

The video tutorial by Bruce on 'Sine Of Our Time' covers adding polynomials using two methods: horizontal and vertical. It begins with an introduction to like and unlike terms, followed by a detailed explanation of the horizontal method, which involves highlighting like terms and adding them. The vertical method is then demonstrated, using columns for each degree of the variable. An example with three polynomials is provided, showing both methods. The video concludes with a summary, emphasizing that both methods yield the same result, and the choice of method is a personal preference.

What are like terms in polynomials?

• Terms with different variables

• Terms with exactly the same variables

• Terms with the same coefficients

• Terms with the same exponents

Which of the following pairs are like terms?

• x and x^2

• 3x and 8x

• x^2 and x^3

• 4x and 4x^2

What is the first step in the horizontal method for adding polynomials?

• Arrange the terms in descending order

• Write the polynomials in brackets

• Highlight the like terms using different colors

• Add the coefficients directly

When using the horizontal method, why is it not necessary to write polynomials inside brackets?

• Because it makes the calculation easier

• Because the plus sign has no effect on the signs of the terms

• Because it is a rule of algebra

• Because it helps in identifying like terms

In the vertical method, what is a placeholder?

• A term that is not added

• A term with a value of one

• A term with the highest degree

• A term used to fill gaps in columns

What is the sum of 11x^3 and 4x^3 using the vertical method?

• 15x^3

• 7x^3

• 5x^3

• 14x^3

When adding three polynomials using the horizontal method, what is the first step?

• Write the polynomials in descending order

• Highlight all of the like terms

• Add the constant terms

• Add the terms with the highest degree

What is the sum of the terms containing a^3 in the example of adding three polynomials?

• 10a^3

• 7a^3

• 12a^3

• 5a^3

In the vertical method, what should you do if you don't like to see gaps in any of the columns?

• Leave the gaps as they are

• Ignore the gaps

• Add placeholders

• Rewrite the polynomials

What is the final sum of the constant terms in the example of adding three polynomials using the vertical method?

• 2

• 1

• -1

• 0