Multiplying Polynomials: Key Concepts and Techniques

Why can't the FOIL method be used for multiplying a binomial by a trinomial?

• Because FOIL can be used for any polynomial multiplication.

• Because FOIL is exclusively for binomial by binomial multiplication.

• Because FOIL only applies to trinomial by trinomial multiplication.

• Because FOIL is a simplified version of the distributive property.

What property is primarily used to multiply a binomial by a trinomial?

• Identity Property

• Associative Property

• Distributive Property

• Commutative Property

What is the result of multiplying 5a by 4a^2?

• 20a^2

• 20a^3

• 9a^2

• 9a^3

After combining like terms, what is the coefficient of the a^2 term?

• 7

• 8

• 15

• -3

What is the final simplified form of the polynomial multiplication?

• 20a^3 + 7a^2 - 11a + 2

• 15a^3 + 8a^2 - 6a + 2

• 20a^3 - 7a^2 + 11a - 2

• 15a^3 - 8a^2 + 6a - 2

What analogy is used to explain the alternative method of polynomial multiplication?

• Comparing it to addition of polynomials

• Comparing it to division of numbers

• Comparing it to the distributive property

• Comparing it to multiplication of numbers

In the alternative method, where is the -6a term placed?

• In the a^0 place

• In the a^1 place

• In the a^2 place

• It is not included

What is the coefficient of the a^3 term in the final answer?

• 4

• 20

• 15

• -5

What is the final constant term in the simplified polynomial?

• 1

• 0

• -2

• 2

How many steps are involved in the alternative method of polynomial multiplication?

• It varies based on the polynomial

• Four steps

• Three steps

• Two steps