Earlier, you learned to solve linear equations (equations where the highest power is 1) and quadratic equations (equations where the highest power is 2). In this section you’ll learn to solve equations with powers of all possible values. You’ll mainly look at cubic and quartic equations—the method is the same for both.
Theory
Rule
Example 1
Solve the equation
Example 2
Solve the equation
Now you use the zero product property to find the solutions:
Rule
Example 3
Solve the equation
Now, you’ll have to guess a solution. Begin with :
Lucky for you, the first solution you guessed was correct. (You often start with 1 when you guess a solution, and this is why).
Now you have to use polynomial long division on the equation with . Because the expression lacks the -term, you put in an extra space where the -term would have been, or put 0 in front of in the long polynomial division. It’s easier to maintain control over the terms this way.
you get the answers and . Put them in the factorization formula so that the factorization becomes