High School Math : Finding Zeros of a Polynomial

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #12 :Pre Calculus

Find the zeros of the following polynomial:

Possible Answers:

Correct answer:

Explanation:

First, we need to find all the possible rational roots of the polynomial using the Rational Roots Theorem:

Since the leading coefficient is just 1, we have the following possible (rational) roots to try:

±1,±2,±3,±4,±6,±12,±24

When we substitute one of these numbers for, we're hoping that the equation ends up equaling zero. Let's see ifis a zero:

Since the function equals zero whenis, one of the factors of the polynomial is. This doesn't help us find the other factors, however. We can use synthetic substitution as a shorter way than long division to factor the equation.

Now we can factor the function this way:

We repeat this process, using the Rational Roots Theorem with the second term to find a possible zero. Let's try:

When we factor using synthetic substitution for, we get the following result:

Using our quadratic factoring rules, we can factor completely:

Thus, the zeroes ofare

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