Can someone describe the strategy for factoring a polynomial? Please give an example showing all of the steps. Thanks.
I searched Google under the key words "factor polynomial" to get these possible sources:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm
(Broken Link Removed)
http://mathforum.org/dr.math/faq/faq.learn.factor.html
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
please can you describe strategy for factoring a polynomial , give an example showing all of your steps.
thank you
Factoring a polynomial involves breaking it down into smaller, simpler expressions. Here's a step-by-step strategy to factor a polynomial:
1. Identify the type of polynomial: Determine if the polynomial is a binomial (2 terms), trinomial (3 terms), or has even more terms.
2. Find the greatest common factor (GCF): Look for any common factors shared by all the terms. The GCF is useful for factoring out common terms.
3. Factor out the GCF: Divide each term by the GCF and write it outside the parentheses. This reduces the polynomial to a simpler form.
4. Check for special factoring patterns: Look for patterns such as the difference of squares or the perfect square trinomial.
5. Use factoring techniques specific to the polynomial type:
- For a binomial: If the binomial is a difference of squares, use the formula (a^2 - b^2) = (a + b)(a - b).
- For a trinomial: Look for common binomial factors or factor by grouping.
6. Apply the factoring method chosen in step 5: Continue factoring until the polynomial can no longer be factored.
7. Verify the factoring: Multiply the factored terms to ensure they equal the original polynomial.
Let's illustrate this strategy with an example. Consider the polynomial: x^2 + 3x - 4.
Step 1: Identify the type of polynomial - Trinomial.
Step 2: Find the GCF - In this case, GCF is 1 (no common factors).
Step 3: Factor out the GCF - The polynomial remains the same.
x^2 + 3x - 4.
Step 4: Check for special factoring patterns - None applicable.
Step 5: Use trinomial factoring technique.
Step 6: Factor the trinomial - Find two numbers that multiply to the constant term (-4) and add up to the coefficient of the linear term (3).
In this case, the numbers are 4 and -1: 4 * (-1) = -4, 4 + (-1) = 3.
Split the middle term using these numbers: x^2 + 4x - x - 4.
Step 7: Factor by grouping - Group the terms with common factors and factor them separately.
(x^2 + 4x) - (x + 4).
Factor out the GCF from each group: x(x + 4) - 1(x + 4).
Combine the factored terms: (x - 1)(x + 4).
Verification: Multiply the factored terms - (x - 1)(x + 4) = x^2 + 4x - x - 4 = x^2 + 3x - 4 (original polynomial).
Therefore, the factored form of the polynomial x^2 + 3x - 4 is (x - 1)(x + 4).