Solving zero-product property problems

Yea, once again, im lost, my teacher from algebra 1 sucked, didnt even teach us this. so can someone please teach me how to do it / show me?

here is an example from the paper

x^2 - 18x + 81 = 0

im so confused!!!
please help

Thanks
~grant

In order to do this problem you need to use either the quadratic formula or factor. Personally, I prefer to factor, as I find it to be less time consuming. Not all quadratic formulas can be factored, though this one can.

Here is an example of how to factor a quadratic equation, hopefully you can follow along. =)

y = x[sup:yeovbmia]2[/sup:yeovbmia] - 8x + 16

The coefficient in front of x[sup:yeovbmia]2[/sup:yeovbmia] is one. I then multiply that by c, which is 16 in this situation. 1 x 16 = 16.

I then need to find two numbers that are divisible by 16 that equal b, which is -8 in this situation, when they are added together.

-4 + -4 = -8
-4 x -4 = 16

So then I am going to use a box, which I'm not sure if you have ever used before, but I find this much simpiler than foiling.. especially when you are going backwards.

______ ______

_____ x[sup:yeovbmia]2[/sup:yeovbmia] -4x

_____ -4x 16


I then want to see what is common to fill out the spaces above the box.

x -4

x x -4x

-4 -4x 16

This equation factors out to (x-4)[sup:yeovbmia]2[/sup:yeovbmia].

When I set x - 4 to equal zero, I discover that the solution is 4. There is only one solution to this problem because the factor has a multiplicity.

I'm not sure how understandable this will be, as it's easier for me to show someone how to do an equation in person, but hopefully you will get some use out of this. Let me know if there is anything that needs to reexplained.

mogfog said:

Yea, once again, im lost, my teacher from algebra 1 sucked, didnt even teach us this. so can someone please teach me how to do it / show me?

Click to expand...

It is unfortunate that you are being tested on material that was never covered in any of your classes, nor mentioned in any of your textbooks. You might want to have a serious talk with your academic counsellor, or with your school's administration, regarding this issue. (Legal counsel may be advisable!)

Unfortunately, it is not reasonably feasible to attempt to provide the missing weeks or months of classroom instruction within this environment, so you will need to attempt some self-study, or else hire a tutor. If you'd like to try learning this online, and assuming that you're fully comfortable with variables, formulas, and solving linear and literal equations, you might want to start with the following sequence of topics:

. . . . .Google results for "simple factoring"

. . . . .Google results for "factoring quadratics"

. . . . .Google results for "factoring trinomials"

. . . . .Google results for "special factoring difference squares cubes"

. . . . .Google results for "quadratic formula"

. . . . .Google results for "solving quadratic equations"

Once you have studied at least two lessons from each link, working through all of the examples until you understand them, please attempt the exercise. If you get stuck, kindly please reply with a clear listing of your work and reasoning so far, so that we may attempt to find the remaining gaps in your background, and try to help you get caught up with your school's current expectations. :idea:

Please be complete. Thank you!

Eliz.