Multiplying a Polynomial by a Monomial:

When multiplying a polynomial by a monomial there are usually parentheses involved. We say that the parentheses hold the "quantity" being multiplied by the monomial.

ex: is read, "Three x times the quantity x plus four."

What you need to keep in mind is that the 3x is being multiplied times EVERYTHING inside of the quantity, not just the x. Technically this is called the distributive property of multiplication over addition.

So our problem becomes, . Which is equal to .

Keep in mind all of the rules for multiplying monomials, raising monomials to a power, adding polynomials, and subtracting polynomials as you simplify these problems.

Give these warm-ups a try. Click on the answer links to see if you are correct.
Good luck.

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