SOLUTION: Hello, can you please help me solve these two problems :) Find the solution set. Write answer in interval notation. x^3(X-2)^2(x+3)< 0 I tried to FOIL the squared quantity

Question 473098: Hello, can you please help me solve these two problems :)
Find the solution set. Write answer in interval notation.
x^3(X-2)^2(x+3)< 0
I tried to FOIL the squared quantity, which is a different of squares
(x-2)(x+2), which gave me x^2-2x+2x- 4
then i tried multiplying the quantity (x+3)by (x^2-4)
my answer ca out to be x^6 + 3x^4-4x^3+ 12x^2. I know this isnt correct?
Help please )
Next question is Graph the Function. Specify the x-intercept, y-intercept, asymptote, domain and range.
f(x)= 7^x
Please help. Thank you! :)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^3(X-2)^2(x+3)< 0
---
Draw a number line.
Plot x = -3, x = 0, x = 2
Note: Those are value x cannot take as they
would make the left side = 0.
===================================
Test a value from each of the number line intervals
to see where the solutions lie:
----------
x^3(X-2)^2(x+3)< 0
Test x = -10, -*-*- < 0 ; true, so solutions in (-oo,-3)
----
Test x = -1, -*-*+ < 0 ; false
---
Test x = 1, +*-*+ < 0 ; true, so solutions in (0,2)
----
Test x = 10, +*+*+ < 0; false
==========================
Solution: (-oo,-3)U(0,2)
===================================================
Next question is Graph the Function. Specify the x-intercept, y-intercept, asymptote, domain and range.
f(x)= 7^x
x-int: Let y = 0, (there is no x-value that will make y = 0)
---
y-int: Let x = 0, then y = 1
---
Asymptote: y = 0
---
Domain: All Real Numbers
---
Range: All Real Number greater than 0
==================

===============
Cheers,
Stan H.

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