simplifying expressions
gcf greatest common factor
factorizing expressions
To factorize expressions, you must first find the GCF (greatest common factor) of all parts of the expression. After finding this, write the value as the beginning of the new expression, and write in parenthesis whats left, after it has been divided by its GCF.
*A way of checking your answer is using the distributive property to expand your answer, and if it matches the expression that you began with, then the answer is correct. |
foil
factorizing trinomial expressions
When you factorize trinomials, you are rewriting the expression as two binomials. You could say this is the opposite of the FOIL method. The expression must be written in the form of ax + bx + c = 0. Then you must find two factors that when multiplied together will give you the "c" value in the equation, and when combined, give you the "b" value in the equation.
*A way to check your answer, is to use the FOIL method, and if you get the original equation, your factorisation process was accurate |
null factor law
When the product of an equation is 0, then at least one must be 0. This means that when two numbers are multiplied, and give a product of 0, one of these numbers must be 0.
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In this example, you are multiplying 2x and the result of (x - 1), and the product of these give you 0. If you connect this to the null factor law, at least one of the elements of the equation must be 0. So we use this to find the solutions for x.
In order for 2x to equal 0, x = 0 And for (x - 1) to equal 0, x = 1 |
quadratic formula
The quadratic formula is used to solve the value for the unknown value for any equation in the form of ax + bx + c = 0. This is the formula:
Although it may seem complicated, the equation uses operations we are all very familiar with: exponents, multiplication, division, radicals, etc. Most of the times, the formula is used when an equation can not be factorized. After practicing many times, the level of difficulty decreases. The example shows every step that can be taken to ma sure you have an accurate answer,.
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unit reflection
I wouldn't consider this unit hard, but I do consider it one where you had to practice in order to succeed. Many of the concepts involved topics we had studied and learned before, and many others were new, but there were definitely many parts that involved the commitment to practice, to be able to really learn the concept. Simplifying expressions, factoring equations, and finding the GCF were concepts that I understood and had no problem with them in class. The FOIL method was something new, that I had to practice several classes to do them easily. By the end of the unit, I was even able to use the method mentally,to some specific equations. THe hardest part of the unit was the quadratic formula, since that was a totally new concept for me. And although it involved simple operations, it had many steps that could change the answer with one simple mistake. I struggled with this for the first classes, and by the end, I was able to do them correctly, checking every step to avoid making small mistakes.
***REAL LIFE APPLICATION: Practicing so much finding the greatest common factor for numbers, has made me realise how different objects can have common characteristics, like shape, colors, texture, etc.
***REAL LIFE APPLICATION: Practicing so much finding the greatest common factor for numbers, has made me realise how different objects can have common characteristics, like shape, colors, texture, etc.