Mathematics

Factoring

Learning Goals:

By the end of this unit I will understand:

1) How to simplfiy quadratics

2) How to factor common coeffcients and variables

3) How to graph a quadratic equation

4) How to solve word problems related to factoring quadratics

Summary

There are six different type of factoring.


The first one is common factoring. For example a question will be like: x^2 + 7x. 1st thing you must do is find what variable os common in this equation. As you can see x is the common variable in the equation so then what you do is put x on the outside and place brackets on the inside like so : x (x+7). Because x was common I took it out and i factored it


The next factoring is common + simple. For example a question will be like 4x^2 - 28x +48. What you do hear is you first find the common variable in all of the coefficients. Then you place the common dividable number on the outside of the brackets. Then you find out what two numbers add up to -7 and multiple into 12. Once that is found the next step will be to make two brackets out of those numbers and from that you will find your answer to be:

4(x-3)(x-4)


The next factoring is called complex trinomials. Nothing much is different compared to common simple factoring. As long as you understand the other factoring this one will be fine.


Now come the last ones which are difference of squares and common + difference of squares. As long as you understand difference of squares adding the common wouldn't change much. For example a difference of squares question would be like x^2 - 16. For you to identify that this is difference of squares it is shown by the middle sign. If that sign is minus then it is a difference of squares as well as if there are only two numbers in that equation. What you do is you square root the entire equation so it will be x - 4. After that there will be two brackets one of which is going to be x- 4 and the other one being x + 4. This is why it is called the difference of squares because there are two different signs. And lastly to find the common diff. of square you just take the common factor out 1st then do the difference of squares.

Word Problems

Problem: The height, h, in meters of a toy rocket at any time, t, in seconds during its flight can be estimated using the formula h=-5t^2-23t+10. What is the initial height of the golf ball?

To put it simple to find the initial height of the golf ball all that is required is to substitute t=0. This is because at the initial height there is no time being evolved with the equation so simply substitute it to 0. From this the answer will be looking like h=-5(0)^2-23(0)+10. Then you simplify the equation and the answer will be h= 10 meters. Therefore the initial height of the golf ball will be 10 meters above the ground.