Combining and Simplifying Polynomials

This video tutorial covers the addition and subtraction of polynomials, emphasizing the similarity to simplifying algebraic expressions. It explains the steps involved, such as using the distributive property to eliminate parentheses and combining like terms. The tutorial provides examples to illustrate these concepts, ensuring a clear understanding of polynomial operations.

What is the first step in simplifying algebraic expressions?

• Multiply by zero

• Use the distributive property

• Simplify within the parentheses

• Combine like terms

When adding polynomials, what can you do with the parentheses?

• Divide them

• Drop them

• Add them together

• Multiply them by zero

What is the highest degree term in the polynomial 3n^2 - 2n + 8 + 3n^3 - 7n^2 - n - 9?

• n

• Constant

• n^3

• n^2

What is the result of combining the terms 3n^2 and -7n^2?

• 10n^2

• -4n^2

• 0

• 4n^2

What is the purpose of distributing a negative one when subtracting polynomials?

• To add the terms

• To multiply the terms

• To ensure each term in the second polynomial is subtracted

• To divide the terms

In the expression a^3 + 5a + 11 - 4a^3 - 6a^2 + a - 1, what is the coefficient of the a^3 term after combining?

• 1

• 0

• -3

• 4

What happens to the terms -1x^2 and 1x^2 when combined?

• They add up to 2x^2

• They remain unchanged

• They cancel each other out

• They subtract to -2x^2

In the expression 3x - 1 + x^2 + x + 9 + x^3 + x^2 - 7x + 2, what is the highest degree term?

• Constant

• x

• x^3

• x^2

What is the result of combining the terms 3x, x, and -7x?

• 5x

• -3x

• 0

• 7x

What is the final constant term in the expression -1 + 9 + 2?

• 8

• 0

• 12

• 10