# High School Math : Understanding Zeros of a Polynomial

## Example Questions

### Example Question #1 : Understanding Zeros Of A Polynomial

Factor the polynomial if the expression is equal to zero when .

Explanation:

Knowing the zeroes makes it relatively easy to factor the polynomial.

The expression fits the description of the zeroes.

Now we need to check the answer.

We are able to get back to the original expression, meaning that the answer is .

### Example Question #2 : Understanding Zeros Of A Polynomial

A polyomial with leading term  has 6 as a triple root. What is this polynomial?

Explanation:

Since 6 is a triple root, and the degree of the polynomial is 3, the polynomial is , which we can expland using the cube of a binomial pattern.

### Example Question #3 : Understanding Zeros Of A Polynomial

A polyomial with leading term  has 5 and 7 as roots; 7 is a double root. What is this polynomial?

Explanation:

Since 5 is a single root and 7 is a double root, and the degree of the polynomial is 3, the polynomial is . To put this in expanded form:

### Example Question #4 : Understanding Zeros Of A Polynomial

What are the solutions to  ?

Explanation:

When we are looking for the solutions of a quadratic, or the zeroes, we are looking for the values of  such that the output will be zero. Thus, we first factor the equation.

Then, we are looking for the values where each of these factors are equal to zero.

implies

and  implies

Thus, these are our solutions.