# How to Use a Graph to Factor Polynomials

Factoring polynomials is the process of expressing a polynomial as the product of two or simpler polynomials. One method to factor a polynomial is to use a graph of the polynomial.

## Step-by-Step Guide to Using a Graph to Factor Polynomials

You can use the graph to factor polynomials with the following step-by-step method:

Step \(1\): Draw a polynomial graph using \(x\)-intercepts and \(y\)-intercepts.

Step \(2\): Mark the polynomial zeros on the graph. These zeros correspond to the \(x\)-coordinates of the intersection points with the \(x\)-axis.

Step \(3\): Draw a horizontal line from each zero and find the intersection points with the polynomial graph. These points correspond to the \(x\)-coordinates of the factorization.

Step \(4\): Write the polynomial as \((x – a)(x – b)…(x – z)\). In this relation, \(a\), \(b\), …, \(z\) are the zeros of the polynomial that you identified in step 2.

This method is suitable for real zero polynomials, but it is not applicable for factoring polynomials with mixed zeros.

**Using **a Graph to Factor Polynomials** – Examples**

Here’s an example of how to use a graph to factor a polynomial:

Example: Factor the polynomial 3x^2 + 6x – 9

- Plot the points on the graph: Plot the points (3,-9), (1, -3), and (-1, -9) on the x-y plane.
- Draw a smooth curve through the points: Connect the points with a smooth curve.
- Identify the x-intercepts: The x-intercepts are the points where the curve crosses the x-axis. In this case, the x-intercepts are (1, 0) and (-1, 0).
- Write the factored form: The factored form of the polynomial is the product of two binomials, one with x-intercepts (1,0) and the other with x-intercepts (-1,0).
- Write the polynomial in factored form: (x – 1)(3x – 9) = 3x^2 + 6x – 9

It’s worth noting that this is just one method to factor polynomials, and different polynomials may require different methods to factor. Also, using a graph to factor polynomials can be useful for visualizing the relationship between the factors and the x-intercepts, but it is not always the most efficient method for factoring polynomials, specially for polynomials with high degree or more complex.

## Related to This Article

### More math articles

- FREE 7th Grade ACT Aspire Math Practice Test
- Geometry Puzzle – Challenge 72
- 4th Grade Mathematics Worksheets: FREE & Printable
- 5 Signs to Understand You’re Good at Math
- How to Measures of Dispersion?
- Top 10 3rd Grade PSSA Math Practice Questions
- 4th Grade NYSE Math Practice Test Questions
- CLEP College Algebra FREE Sample Practice Questions
- Top 10 8th Grade STAAR Math Practice Questions
- How is the SSAT Test Scored?

## What people say about "How to Use a Graph to Factor Polynomials"?

No one replied yet.