MHB Solving Polynomial Inequalities

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To solve the polynomial inequality $(x - 3)(x + 1) + (x - 3)(x + 2) \ge 0$, first factor the left-hand side to get $(x-3)(2x+3) \geq 0$. Identify the zeros of the function, which are at $x=3$ and $x=-\frac{3}{2}$. Create an interval table to determine where the product $(x-3)(2x+3)$ is positive. The solution will be the intervals where the function is greater than or equal to zero.
eleventhxhour
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Solve the following inequality:

6e) $(x - 3)(x + 1) + (x - 3)(x + 2) \ge 0$

So, I created an interval table with the zeros x-3, x+1, x-3 and x+2 but I keep getting the wrong answer. Could someone help? (this is grade 12 math - so please don't be too complicated).

Thanks.
 
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I would start with factoring the LHS:
$$(x-3)[(x+1)+(x+2)] \geq 0$$
$$\Leftrightarrow (x-3)(2x+3) \geq 0$$

Now create an interval table and look where the function $f(x)=(x-3)(2x+3)$ which has two zeros at $x=3$ and $x=\frac{-3}{2}$ is positive. That will give you the answer.
 
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