By Sarah Glidden
This newsletter I will be explaining a few different methods that can be used to factor a polynomial. I will explain factoring by grouping, the quadratic formula, and completing the square. These methods will be very helpful when needing to solve basic or very complex polynomials.
Factor by Grouping
Factoring by grouping is used when you have 4 terms in the polynomial. Here are the steps needed:
- In order to factor take the first two terms and find a GCF or greatest common factor.
- Then do the same for the third and forth term.
- Now you take the GCF's of the two groups and put them together to create a binomial and solve for X.
- The other binomials left after the GCF's is factored out should be solved for X to get your two answers. ( The binomial left from each group should always be the same or else something was done wrong)
Quadratic Formula can be used to solve any quadratic equation. This is very helpful when the basic cross- box method of factoring does not work. Follow the steps below to use the formula successfully.
- First write out the equation out in standard form (ax^2+bx+c=0)
- Then plug in the values of the equation into the formula (see example for formula)
- Now simplify the equation as far as possible
- now solve for the solutions (Once done simplifying you should have two solutions because there is a square root in the equation)
*See the example below for a better understanding.
Completing the Square
Completing the square is a process used to solve for x in a quadratic equation but this process is normally faster than using the quadratic formula. See the steps below to use completing the square.
- First make sure the equation is in standard form (ax^2 + bx + c = 0)
- Then move the c value of the equation to the right of the equal sign
- Now divide every term by the a value (Note: this step is not necessary if a=1)
- Next take half the b value and square it
- Now take this value an add it to both sides
- Then you simplify the left side into a perfect square
- Lastly solve the equation for x ( you should get two solutions)
*See the example below for more explantation
Monday December 7th → Quiz 4
Thursday December 10th → Test 2