SOLUTION: I have to graph the following equation: {{{ y= (x-3)^9(x+5)^8(8x-7)^3 }}} I have tried factoring out x and I am just not sure if you can use the FOIL method with three polynom

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to graph the following equation: {{{ y= (x-3)^9(x+5)^8(8x-7)^3 }}} I have tried factoring out x and I am just not sure if you can use the FOIL method with three polynom      Log On


   

Question 326022: I have to graph the following equation: +y=+%28x-3%29%5E9%28x%2B5%29%5E8%288x-7%29%5E3+
I have tried factoring out x and I am just not sure if you can use the FOIL method with three polynomials. Plus all three of them are multiplied together, and then have an exponant, so when I try to plug in a number for x, I get a huge number for y.
Thanks for any help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, you can't factor the x out of any of the factors.
It's as simplified as it can get.
Approach it from a different perspective.
Since it's in this form, you can easily pick out the zeros.
x-3=0
x=3
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x%2B5=0
x=-5
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8x-7=0
8x=7
x=7%2F8
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So for those 3 points the equation equals zero.
Now look at point immediately before and after those points and see if they are positive or negative. Don't worry about the exact value.
x=-6
%28-6-3%29%5E9%28-6%2B5%29%5E8%288%28-6%29-7%29%5E3+
The first and third terms are negative, second term positive, so the product is positive.
x=-4
%28-4-3%29%5E9%28-4%2B5%29%5E8%288%28-4%29-7%29%5E3+
Same as with x=-6
So you know that curve comes down from a big positive number, just touches the x-axis at x=-5, and then returns to a big positive number.
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Move on to x=7%2F8
x=0
%280-3%29%5E9%280%2B5%29%5E8%280-7%29%5E3+
Same as above, the product is positive.
x=1
%281-3%29%5E9%281%2B5%29%5E8%288-7%29%5E3+
The first term is negative, the others positive, the product is negative.
So the curve comes down from a big positive number, equals zero at x=7/8, then proceeeds to a large negative number.
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Move on to x=3
x=2
%282-3%29%5E9%282%2B5%29%5E8%288%282%29-7%29%5E3+
Same as x=1, negative product.
x=4
%284-3%29%5E9%284%2B5%29%5E8%288%284%29-7%29%5E3+
All terms are positive, positive product.
The curve starts negative, equals zero at x=3, then proceeds to a large positive number.
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NOTE: The graph has been altered by not plotting the actual y values to show some slope in the lines. Due to the multiple powers, the numbers get very large very quickly. If I had plotted them with real values, the line would have looked like vertical lines in all cases and you would have missed what's really going on. As an example, the value of x=2.8 is y=-25620.6.