Understanding Polynomial Multiplication

What is the key property used in multiplying polynomials?

• Commutative Property

• Distributive Property

• Identity Property

• Associative Property

When multiplying a monomial by a polynomial, what is the first step?

• Combine like terms

• Distribute the monomial across each term of the polynomial

• Multiply the coefficients

• Add the coefficients

In the expression (4x + 5)(3x + 2), what is the result of distributing 3x?

• 6x^2 + 10x

• 12x^2 + 15x

• 8x + 10

• 7x + 14

What is a common mistake when squaring a binomial like (x - 3)^2?

• Forgetting to distribute the negative sign

• Squaring each term individually

• Adding the terms instead of multiplying

• Multiplying each term by 2

How should (x - 3)^2 be correctly expanded?

• x^2 - 3x + 3

• x^2 - 6x + 9

• x^2 + 6x + 9

• x^2 - 9

What is the first step in multiplying a binomial by a trinomial?

• Combine like terms

• Distribute each term of the binomial across the trinomial

• Add the coefficients

• Subtract the exponents

In the expression (x + 2)(x^2 - 3x + 7), what is the result of distributing x?

• x^3 - 3x^2 + 7x

• x^2 - 3x + 7

• x^3 + 2x^2

• x^2 + 3x + 7

What is the result of combining like terms in the expression x^3 - x^2 + x + 14?

• x^3 - 2x^2 + 2x + 14

• x^3 - x^2 + x + 14

• x^3 + x^2 + x + 14

• x^3 - x^2 + 2x + 14

What is the result of distributing 2 in the expression (x + 2)(x^2 - 3x + 7)?

• 2x^2 + 6x + 14

• 2x^2 - 3x + 7

• 2x^2 + 3x + 14

• 2x^2 - 6x + 14

What is the final result of multiplying (x + 2)(x^2 - 3x + 7)?

• x^3 - 3x^2 + 7x + 14

• x^3 - x^2 + x + 14

• x^3 - x^2 + 2x + 14

• x^3 - x^2 + x + 14