# Finding Zeros of Polynomial Functions Worksheets

We can transform equations of interest into equivalent equations that have one side equal to zero. So, if we can get that one side to be equal to zero, we can solve it for other cases as well. The zero of polynomials is very helpful because it allows use to determine the root. When you are able to rearrange an equation to perform this and then couple it with a well-known formula, you can usually solve for the value of any unknown variables within it. This is especially helpful for solving quadratics. These worksheets and lessons help students locate and understand how to find a root of a polynomial. These are values of x or y that cause the polynomial to equal zero.

### Aligned Standard: HSA-APR.B.3

- Zero Products Step-by-step Lesson- We show you an effective means for determine the possible values for a product that equals zero.
- Guided Lesson - Working through these types of problems will give you a great deal of time to understand the rearrangement of equations.
- Guided Lesson Explanation - We go over the concept of Zero Product Properties and how they relate to finding missing variable values.
- Practice Worksheet - Work away at this skills by tackling ten nicely developed problems.
- Matching Worksheet - We used f as every variable to make it much more challenging. Different variable would have just made it too easy.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

This is a true fundamental skill that students need to master for higher grade level work.

- Homework 1 - We know that the Zero Product Property states that for all real numbers a and b: If ab = 0, then a = 0 or b = 0
- Homework 2 - According to the Zero Product Property, if (t - 62) (t - 17) = 0, then (t - 62) must be 0 or (t - 17) must be 0.
- Homework 3 - Solve for p and write your answers as whole numbers in the simplest form.

### Practice Worksheets

Some of the addends in here are huge on purpose.

- Practice 1 - Write your final outcome in the simplest form.
- Practice 2 - Where does d equal zero?
- Practice 3 - Solve for b and write your answers as whole numbers in the simplest form.

### Math Skill Quizzes

See if you think version 3 is challenging? I got asked to make that version slightly easier. I'm not sure why.

- Quiz 1 - Find the values of g (g – 12) (g – 45) = 0
- Quiz 2 - We use large integers here.
- Quiz 3 - Get everything in one side.

### How to Identify Zeros of Binomials?

Let us first determine what root or a zero of a polynomial is. The root of the polynomial means that by solving a function, you will get a non-zero answer. This value is called the root of a function. However, if by solving a function, your answer is 0, then that means you get no value for solving it.

Now, a binomial function means that in a given equation, two unknowns are present. Now, we will find out how we can identify a zero in a binomial equation. Let us take an example of y = x^{2} + 2x - 15. First, we need to solve the equation to find out its roots. Let us consider y as zero for solving this problem.

x^{2} + 2x – 15 = 0, x^{2} + 5x - 3x - 15 = 0, (x + 5) (x - 3) = 0

Now, if we write the last equation separately, then, we get: (x + 5) = 0, (x - 3) = 0

Both separate equations can be solved as roots, so by placing the constants from the left-hand side of the equal sign to the right-hand-side, the signs will change. The resultant values will be:

x = 3, x = -5

If we look at it objectively, the binomial equation had two zeros and two roots. Similarly, we can solve other binomial equations as well.

### How Do You Find the Zeros of a Polynomial?

The easiest way to do this is to factor the polynomial into linear factors but is not always applicable. Always begin by listing all the possible rational zeroes by using the Rational Zero Theorem. We then apply an available synthetic division operations to see if we have any other potential contenders. If it is a 0, it is in the running otherwise it is not. You can continue on with this until you form a quadratic and then determine any remaining zeroes with the quadratic formula.