Polynomial Operations and Distributions

The video tutorial covers polynomial addition and multiplication, focusing on distributing terms, performing multiplications, and combining like terms. Three problems are solved step-by-step: multiplying polynomials, simplifying expressions with multiple terms, and simplifying a complex expression. The tutorial emphasizes the repetitive nature of the process and encourages students to practice to catch small mistakes.

What is the first step in polynomial addition and multiplication?

• Combining like terms

• Distributing

• Factoring

• Simplifying

In the expression (4X^3 - 5X^2 - 3X + 7) * (2X - 5), what is the result of distributing 4X^3?

• 8X^3 - 20X^2

• 8X^4 + 20X^3

• 8X^4 - 10X^3

• 8X^4 - 20X^3

What is the result of combining the like terms -20X^3 and -10X^3?

• -10X^3

• -40X^3

• -30X^3

• -20X^3

What is the final simplified form of the expression (4X^3 - 5X^2 - 3X + 7) * (2X - 5)?

• 8X^4 - 20X^3 + 19X^2 + 29X - 35

• 8X^4 - 30X^3 + 19X^2 + 29X - 35

• 8X^4 - 30X^3 + 19X^2 + 29X + 35

• 8X^4 - 30X^3 + 19X^2 + 14X - 35

In the expression 3 * (2X - 5) * (X^2 - 4X + 2), what is the result of multiplying 3 and (2X - 5)?

• 3X + 5

• 6X - 15

• 6X + 15

• 3X - 5

What is the result of distributing 6X in the expression (6X - 15) * (X^2 - 4X + 2)?

• 6X^3 + 24X^2 - 12X

• 6X^3 - 24X^2 - 12X

• 6X^3 + 24X^2 + 12X

• 6X^3 - 24X^2 + 12X

What is the final simplified form of the expression 3 * (2X - 5) * (X^2 - 4X + 2)?

• 6X^3 - 39X^2 + 72X - 30

• 6X^3 - 39X^2 + 60X - 30

• 6X^3 - 24X^2 + 72X - 30

• 6X^3 - 39X^2 + 72X + 30

In the expression (3X - 1) * (-2X^2 + 4X - 7), what is the result of distributing 3X?

• -6X^3 - 12X^2 - 21X

• -6X^3 + 12X^2 + 21X

• -6X^3 - 12X^2 + 21X

• -6X^3 + 12X^2 - 21X

What is the result of combining the like terms 12X^2 and 2X^2?

• 10X^2

• 14X^2

• 12X^2

• 16X^2

What is the final simplified form of the expression (3X - 1) * (-2X^2 + 4X - 7)?

• -6X^3 + 12X^2 - 25X + 7

• -6X^3 + 14X^2 - 21X + 7

• -6X^3 + 14X^2 - 25X - 7

• -6X^3 + 14X^2 - 25X + 7