Adding and Subtracting Polynomials

The video tutorial introduces polynomials, explaining their structure and how to perform basic operations like addition and subtraction. It emphasizes the importance of combining like terms and using the distributive property. Examples are provided to illustrate the process of adding and subtracting polynomials, ensuring terms are aligned correctly. The tutorial concludes with a brief mention of multiplication, setting the stage for more complex operations.

What is a polynomial?

• An expression with variables raised to negative exponents

• An equation with only constant terms

• An expression with variables raised to positive whole number exponents

• An equation with no variables

When adding polynomials, what is the key step?

• Reversing the order of terms

• Multiplying all terms by a constant

• Combining like terms

• Dividing each term by its exponent

In the expression 5x^3 + 4x^3, what is the result of combining like terms?

• 20x^3

• 1x^3

• 9x^6

• 9x^3

What is a tidy approach to adding two polynomial expressions?

• Writing them in a single line without aligning terms

• Aligning terms by their exponents and adding vertically

• Subtracting the smaller polynomial from the larger one

• Ignoring the exponents and adding coefficients

What is the result of adding 4x^3 + 2x^2 - 6x + 9 and x^4 - 3x^2 + 6x - 4?

• x^4 + 4x^3 - x^2 + 5

• x^4 + 4x^3 + 5x^2 + 5

• x^4 + 4x^3 - 9x + 5

• x^4 + 4x^3 - x^2 - 5

When subtracting polynomials, what must you be careful about?

• The degree of the polynomials

• The signs of the terms

• The coefficients of the terms

• The order of terms

What is the result of subtracting x^4 - 3x^2 + 6x - 4 from 4x^3 + 2x^2 - 6x + 9?

• -x^4 + 4x^3 + 5x^2 - 12x + 13

• x^4 + 4x^3 + 5x^2 - 12x + 13

• -x^4 + 4x^3 - 5x^2 + 12x - 13

• x^4 - 4x^3 + 5x^2 + 12x - 13