SOLUTION: I need help with this problem,,, f(x)=(x-2)^2(x+1)(x-5)=0 The question wants me to start the problem by simplifying into polynomial form. I've tried the FOIL method and its just

Question 323495: I need help with this problem,,, f(x)=(x-2)^2(x+1)(x-5)=0 The question wants me to start the problem by simplifying into polynomial form. I've tried the FOIL method and its just not working out.
The online course does give an example, but I can't see how they "solved" or got too the example. lol I need an example of the example.
Here is the example:
(x-2)^2(x+1)(x-5)=0
x^4-8x^3+15x^2+4x-20=0 I need to see how they came to this point. Once I see that I will be ok. This is apart of a problem wanting me to graph the polynomial function.
I really appreciate the help.
Thank you,
Tom Adkins

Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
Hi Tom,
You were correct in using the FOIL method for this problem, you will use this method 3 times.
First rewrite the problem so it is easier to see how to multiply:
(x-2)^2(x+1)(x-5)
=(x-2)(x-2)(x+1)(x-5)
Now we will use the method 3 times. First, multiply out just the (x-2)(x-2):
(x-2)(x-2)(x+1)(x-5)
=(x^2-2x-2x+4)(x+1)(x-5)
=(x^2-4x+4)(x+1)(x-5)
Now multiply (x^2-4x+4)(x+1) using FOIL:
=(x^2-4x+4)(x+1)(x-5)
=(x^3-4x^2+4x+x^2-4x+4)(x-5)
This can be simplified by adding the x^2 values and adding the x values:
=(x^3-3x^2+4)(x-5)
Finally, multiply (FOIL) what is left:
=(x^3-3x^2+4)(x-5)
=(x^4-3x^3+4x-5x^3+15x^2-20)
=(x^4-8x^3+15x^2+4x-20)
So this is your simplified polynomial form:
x^4-8x^3+15x^2+4x-20= 0
I hope this helped! Let me know if you have more questions!
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