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3. Multiplication and Division of Polynomials

# Multiplying polynomials by monomials

In the previous chapter, we learned that Polynomials are expressions that are comprised of a coefficient, a constant, variables and exponents. We also learned that there are different kinds of polynomial expression, namely monomial, binomial and trinomial. We also learned that these terms can be combined through the four different operations namely addition, subtraction, multiplication and division. In the last few chapters we were able to discuss how to add and subtract polynomials, so for this chapter, we will focus a bit more on multiplying and dividing polynomials.

For multiplying polynomials, the rule is very simple, apply distributive property to all the terms to get the product. Say you’re asked to multiply 6x and 5y then this would translate to (6 x 5) + (6 x y) + (x x 5) + (x x y). Simplifying this expression you get 11 + 6y + 5x + xy, rearranging the expression you would get 5x + 6y + xy + 11. If negative integers are present, then make sure you also distribute the sign in order to get the correct answer.

Dividing polynomials on the other hand can be a little easier to do than multiplying them. In dividing polynomials, you are simply reducing the fraction. So if you’re given $9x^{2} /x$ then this would just be 9x because you get to cancel out the x from both the denominator and numerator. If you’re given $6x^{2}-24x/3x$ then you should factor out the numerator such that the denominator would be cancelled out. This equation would be factored out into (2x-8)(3x)/ 3x, so you may now cancel 3x and you get 2x-8.

This chapter is divided into three parts. The first part will be more focused on the general process of multiplying and dividing polynomials. The last two parts would be about multiplying and dividing polynomials with monomials.

### Multiplying polynomials by monomials

This section will teach us how to multiply a polynomial (more than one term) by a monomial (one term only). We will use an area model as an aid to do the multiplication. We will then try to solve the questions without using the model. At the end, we will look at some of the related word problems.