Combining and Distributing Polynomials

This video tutorial teaches how to subtract polynomials by converting subtraction into addition. It reviews the concept of subtraction as adding the opposite and the distribution of terms. The lesson covers combining like terms in polynomial addition and emphasizes the importance of changing all signs when multiplying by negative one. The tutorial also demonstrates simplifying polynomial expressions and using vertical subtraction for large polynomials.

What is the result of changing subtraction to addition in the expression 12 - 8?

• 20

• 4

• 16

• 0

How does distribution work in the expression 5 * (3x + 1)?

• 15x + 1

• 5x + 3

• 3x + 5

• 15x + 5

What is the result of combining like terms in the expression 3x^2 + 10x^2?

• 30x^2

• 7x^2

• 3x^2

• 13x^2

What is a common mistake when multiplying a polynomial by -1?

• Leaving the polynomial unchanged

• Multiplying by 0

• Changing all signs to positive

• Only changing the sign of the first term

What is the correct result of multiplying -1 by the polynomial 4x^2 + 2x - 8?

• -4x^2 - 2x + 8

• 4x^2 - 2x + 8

• 4x^2 + 2x - 8

• -4x^2 + 2x - 8

What is the result of combining like terms in the expression 3x^2 - x^2?

• 4x^2

• 3x^2

• 2x^2

• 0

How do you handle subtraction in large polynomials using vertical subtraction?

• By only changing the first term

• By multiplying by zero

• By ignoring the signs

• By adding the opposite

What is the result of the expression 3x^5 + 2x^4 - 7x^3 + 10x^2 - 9x + 2 - (8x^5 + 9x^4 + 4x^3 - 12x^2 - 6x - 10)?

• -5x^5 + 11x^4 - 3x^3 - 2x^2 - 15x - 8

• 5x^5 - 11x^4 + 3x^3 + 2x^2 + 15x + 8

• 3x^5 + 2x^4 - 7x^3 + 10x^2 - 9x + 2

• 0

What is the first step in vertical subtraction of polynomials?

• Ignore the second polynomial

• Multiply both polynomials by zero

• Add the polynomials directly

• Distribute -1 to the second polynomial

What is the final result of subtracting polynomials by changing subtraction to addition?

• A simplified polynomial

• A more complex polynomial

• An incorrect polynomial

• No change