Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. Polynomials, Linear Factors, and Zeros
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Exercise 4 Page 293

We want to write a polynomial function in standard form with the given zeros. To do so, we will use the Factor Theorem to write the factored form. We will then simplify it by applying the Distributive Property. Let's first recall the Factor Theorem.

Factor Theorem

The expression is a factor of a polynomial if and only if the value is a zero of the related polynomial function.

We know that and are zeros of our function. Therefore, we can write our polynomial function as the product of three factors.
Finally, we can apply the Distributive Property to express the function in standard form.
Simplify right-hand side

Checking Our Answer

Checking Our Answer
We can check our answer by substituting the given zeros for If the result is it means that the given numbers are actually zeros of the function and our answer is correct. Let's start by checking
Evaluate right-hand side
We proved that is a zero of the function. Let's now check
Evaluate right-hand side
We have shown that is also a zero. Finally, let's see what happens with
Evaluate right-hand side
We found that is also a zero. Since and are zeros of the polynomial function, our answer is correct.