On this page we hope to demonstrate the following:
How to multiply polynomials; FOIL method
Ex: (x-2)(x+4) = x2 + 2x - 8
How to factor simple quadratics
Ex: Factor x2 - 4x + 4
How to solve quadratic equations; quadratic formula
Ex: Solve for x: x2 - 4x + 4 = 0
Methods to factor higher degree polynomials.
Ex: Factor x4 - x3 + x2 - 1
When we multiply polynomials, the most important property to remember is the distributive property. If we want to multiply 4 and the term (x + 3), we know that we have to distribute the 4: 4(x+3) = 4x + 12. This is the same principle we follow when we multiply polynomials. We take each entry of our first term and multiply it to the other term, distributing accordingly, and then add up all of the resultant terms.
Example 1: Multiply (x - 2) and (x + 4).
We would like to multiply together two polynomials. To find (x - 2)(x + 4), we distribute each of the entries in the first term, (x - 2), to the second term, (x + 4). So (x - 2)(x + 4) = x(x + 4) + (-2)(x + 4) = x2 + 4x + -2x - 8 = x2 + 2x - 8
Try out the following exercises to get accustomed with multiplying simple polynomials this way.
Find the following products:
1. (2x - 1)(2x - 1) =
2. x(x + 3)(x - 8) =
3. (4x - 3)(3x + 1.25) =