Exploring Polynomial Operations: Addition, Subtraction, and Multiplication

This video tutorial covers the fundamental operations on polynomials, including addition, subtraction, and multiplication. It demonstrates how to perform these operations both vertically and horizontally, emphasizing the importance of combining like terms. The tutorial also explores multiplying three binomials and highlights special cases and shortcuts in polynomial operations.

What is the result of adding 3x^3 + 2x^2 - x - 7 and x^3 - 10x^2 + 8?

• 2x^3 - 8x^2 + x + 1

• 4x^3 - 8x^2 + x + 1

• 4x^3 + 8x^2 - x - 1

• 4x^3 - 8x^2 - x + 1

When adding polynomials vertically, what is the result of 9y^3 + 3y^2 - 2y + 1 and -5y^2 + y - 4?

• 9y^3 - 2y^2 - y - 3

• 9y^3 - 2y^2 + y - 3

• 9y^3 - 2y^2 - y + 3

• 9y^3 + 2y^2 - y - 3

What is the result of subtracting 2x^3 + 6x^2 - x + 1 from 8x^3 - 3x^2 - 2x + 9?

• 6x^3 - 9x^2 - x + 8

• 6x^3 - 9x^2 + x + 8

• 6x^3 - 9x^2 - x - 8

• 6x^3 + 9x^2 - x + 8

What is the result of subtracting 3z^2 + z - 4 from 2z^2 + 3z?

• -z^2 + 2z + 4

• -z^2 + 2z - 4

• z^2 + 2z + 4

• -z^2 - 2z + 4

What is the sum of 2x^2 + 7x^2 and -6x - 1x?

• 7x^2 - 6x

• 9x^2 - 6x

• 9x^2 - 7x

• 7x^2 - 7x

What is the result of multiplying (x - 3) by (-x^2 + 2x + 4)?

• -x^3 + 5x^2 - 2x - 12

• -x^3 - 5x^2 - 2x - 12

• -x^3 + 5x^2 - 2x + 12

• -x^3 + 5x^2 + 2x - 12

What is the result of multiplying y(3y^2 - 2y + 2) and 5(3y^2 - 2y + 2)?

• 3y^3 + 13y^2 - 8y + 10

• 3y^3 + 13y^2 - 8y - 10

• 3y^3 + 13y^2 + 8y + 10

• 3y^3 - 13y^2 - 8y + 10

What is the result of multiplying (x - 1)(x + 4)(x + 5)?

• x^3 + 8x^2 + 11x - 20

• x^3 + 8x^2 + 11x + 20

• x^3 - 8x^2 + 11x - 20

• x^3 + 8x^2 - 11x - 20

What is the result of (a + b)(a - b)?

• a^2 + 2ab + b^2

• a^2 - b^2

• a^2 + b^2

• a^2 - 2ab + b^2

What is the result of squaring a binomial (a + b)^2?

• a^2 + 2ab + b^2

• a^2 - 2ab + b^2

• a^2 + b^2

• a^2 - b^2