<p>How do you go about this problem?</p>
<p>When is (x^2 + 1)(x-2)^2(x-3) greater or equal to zero?</p>
<p>What’s the answer?</p>
<p>Well :</p>
<p>(x^2 + 1) is always going to greater than 0, regardless of the value of x
Likewise with (x-2)^2 </p>
<p>This is because values that are squared will always be positive.</p>
<p>That leaves us with (x-3) > 0</p>
<p>So this is only true when x>3</p>
<p>When x = 2, (x-2)^2 = 0.</p>
<p>Oh yea my bad, that too. so x>2.</p>
<p>No, the question said it can be greater than or equal to zero. So, the answer is x must be greater than or equal to 3.</p>
<p>I’m kind of embarrassed to say this, but to be honest I’d probably just use a graphing calculator for the sake of time…
And I think the answer would be when x=2 and when x is greater than or equal to 3.</p>
<p>Oh wow, that’s really dumb of me.</p>
<p>Now that I look at it, the best way would probably be to make a number line with all the zeros marked. Then test a point in between the intervals denoted by the zeros, to see if they are positive or negative.</p>