Multiplying Polynomials Two Basic Steps
Polynomials are just the sum or powers of x. These powers have to be positive or zero. A few examples are : x^2 + 3x - 7 or 5x^3 + 3x^2 - 12x + 1 or x + 5.
The 'poly' part of polynomial indicates that there are multiple terms in a polynomial. With this, multiplying polynomials breaks down into two parts:
- Multiply each term of one polynomial by every term of the other.
- Combine all of the like terms and write the final answer in standard form of descending powers.
Here is an example most are familiar with that involves multiplying linear factors.
Example 1: 'FOILing'
Consider the following problem.
Multiply the following:
(2x + 3)(x - 7)
The two polynomials in this case are 2x + 3 and x - 7. The terms of the first polynomial are 2x and 3. The terms of the second polynomial are x and -7.
Step 1
We multiply each term of the first by each term of the second:
kkk
Like terms are shaded the same color
Step 2
We combine like terms through addition.
The terms here that are like terms are -14x and 3x. We add these two terms to get -11x. The other terms are left alone. We then write the final answer in standard form with the higher powers written first.
The final answer is:
2x^2 - 11x - 21