4. Solving Polynomial Equations in Factored Form
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Take a look a Exploration 1, Exploration 2, and Exploration 3. What advantages does using the factored form of an equation have?
See solution.
As we can see from Exploration 1, Exploration 2, and Exploration 3, we can write an equation in different forms, one of these is the factored form. An example is shown below.
| Standard Form | Factored Form |
|---|---|
| x^2-4x+3 = 0 | (x-1)(x-3) = 0 |
Recall that any number multiplied by 0 gives 0 as result. Then, each x-value that makes any of the factors to be 0 causes the whole product to be 0 as well, satisfying the equation. For this reason, we can solve an equation in factored by equalizing each factor to zero. x^2-4x+3 = 0 ⇕ (x-1) (x-3) = 0 [1em] cc Solution1 & Solution2 x-1 =0 & x-3 =0 x=1 & x=3 We have found that the solutions for the equation x^2-4x+3 = 0 are x=1 and x=3.