# Precalculus : Polynomial Functions

## Example Questions

### Example Question #6 : Express A Polynomial As A Product Of Linear Factors

Factorize the following expression completely to its linear factors:      Explanation:

Use the grouping method to factorize common terms: ### Example Question #7 : Express A Polynomial As A Product Of Linear Factors

Factorize the following expression completely to its linear factors: f(x)=       Explanation:

Use grouping method to factorize common terms: ### Example Question #8 : Express A Polynomial As A Product Of Linear Factors

Express the polynomial as a product of linear factors:       Explanation:

First pull out the common factor of 2, and then factorize: ### Example Question #1 : Express A Polynomial As A Product Of Linear Factors

Find the real zeros of the equation using factorization: f(x)=   There are no real zeros.   Explanation:

Use grouping to factorize the common terms: ### Example Question #10 : Express A Polynomial As A Product Of Linear Factors

Express the following polynomial as a product of linear factors: Explanation:

First, pull out the common factor of , and then factorize: ### Example Question #11 : Fundamental Theorem Of Algebra

Factorize the following expression completely to its linear factors: Explanation:

Use the grouping method to factorize common terms: ### Example Question #12 : Fundamental Theorem Of Algebra

Factorize the following polynomial expression completely to its linear factors:  Explanation:

Use the grouping method to factorize common terms: ### Example Question #1 : Find Complex Zeros Of A Polynomial Using The Fundamental Theorem Of Algebra

What are the roots of including complex roots, if they exist?     Explanation:

One of the roots is because if we plug in 1, we get 0. We can factor the polynomial as So now we solve the roots of . The root will not be real.

The roots of this polynomial are .

So, the roots are ### Example Question #2 : Find Complex Zeros Of A Polynomial Using The Fundamental Theorem Of Algebra

The polynomial has a real zero at 1.5. Find the other two zeros.      Explanation:

If this polynomial has a real zero at 1.5, that means that the polynomial has a factor that when set equal to zero has a solution of . We can figure out what this is this way: multiply both sides by 2 is the factor

Now that we have one factor, we can divide to find the other two solutions: To finish solving, we can use the quadratic formula with the resulting quadratic,  ### Example Question #1 : Find Complex Zeros Of A Polynomial Using The Fundamental Theorem Of Algebra

If the real zero of the polynomial is 3, what are the complex zeros?      Explanation:

We know that the real zero of this polynomial is 3, so one of the factors must be . To find the other factors, we can divide the original polynomial by , either by long division or synthetic division: This gives us a second factor of which we can solve using the quadratic formula: ### All Precalculus Resources 