Plese can you help me with this:
describe your strategy for factoring a polynomial, give an example showing all of you steps
Check this site.
http://www.purplemath.com/modules/simpfact.htm
Certainly! Factoring a polynomial involves finding the factors that make up the polynomial expression. Here is a general strategy to factor a polynomial along with an example:
1. Identify the common factors: Look for any monomials that can be factored out from each term in the polynomial.
Example: Consider the polynomial 6x^3 + 3x^2 - 12x. In this case, we can factor out the monomial 3x, which is the greatest common factor of all the terms.
Step 1: 3x(2x^2 + x - 4)
2. Check for special factoring patterns: Keep an eye out for special patterns such as perfect squares, the difference of squares, or the sum/difference of cubes. These patterns can often simplify the factoring process.
Example: Let's factor the polynomial x^2 - 4. It can be factored as the difference of squares since it is in the form a^2 - b^2.
Step 2: (x - 2)(x + 2)
3. Apply factoring techniques: If the polynomial doesn't have common factors or special factoring patterns, you'll need to use factoring techniques like the quadratic formula, grouping, or trial and error to factor it further.
Example: Suppose we have the polynomial 2x^2 - 5x + 3. This polynomial cannot be factored using common factors or special patterns, so we'll use the quadratic formula. The quadratic formula states that if ax^2 + bx + c = 0, then x = (-b ± √(b^2 - 4ac)) / 2a.
Step 3: For 2x^2 - 5x + 3, applying the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(2)(3))) / (2(2))
x = (5 ± √(25 - 24)) / 4
x = (5 ± √1) / 4
Simplifying further, we get two factors:
x = (5 + 1) / 4 = 6/4 = 3/2
x = (5 - 1) / 4 = 4/4 = 1
So, the factored form of 2x^2 - 5x + 3 is (2x - 3)(x - 1).
Remember, factoring can sometimes involve trial and error or applying different techniques depending on the complexity of the polynomial. It's always beneficial to practice with more examples to strengthen your understanding.