<p>Ok so my book says: -3^2 = -9 and (-3)^2 = 9
So if x = -3 </p>
<p>x^2 = -9</p>
<p>and</p>
<p>-3x^2 = 27 right?</p>
<p>According to my book -3x^2 = -27 when x = -3</p>
<p>Am I wrong?</p>
<p>The answer should be 27. -3 X -3^2 = ?
-3 X -9 = ?
-3 X -9 = 27</p>
<p>When the -3 is in the parentheses it means you are multiplying -3 x -3, equaling 9. Without the parentheses, you are multiplying 3 x 3, and adding the negative to it, equaling -9. With that idea - </p>
<p>-3^2 = -9</p>
<p>But, every time I’ve seen a question like the -3x^2 = -27, you’re assuming that there are parentheses.
For instance - (3) x (-3)^2. Don’t ask me why.</p>
<p>So:
-3 x (-3)^2 = -27
-3 x 9 = -27</p>
<p>I don’t really know any specific rules about that, sorry, that’s just how I’ve seen it before. I guess it’s like when you solve it out, you would get your answer to be + or - 3, not just +3.</p>
<p>it should be 27. unless it states “The quantity of X squared”, then it will be the negative of the base number, so it would be (-3)^2 = 9 while -3^2 = -9</p>
<p>No, I understand what you’re saying. But, when nothing like that is stated, you’re going to say the answer is + or - 3. Meaning that when x = -3, the answer is -27. I remember going over something like this in the beginning of precalc like 6 months ago, with the alg 2 review. I don’t know why it is, I just know that’s how it works.</p>
<p>There’s implied parenthesis around every variable.</p>
<p>-3x^2 when x = -3
is the same thing as
-3(x)^2 when x = -3
= -3(-3)^2
= -3(9)
= -27</p>
<p>
</p>
<p>No.
x^2 when x = -3
= (x)^2 when x = -3
= (-3)^2
= 9</p>
<p>Then multiplying by a -3 yields (9)(-3) = -27.</p>
<p>So I’m confused and getting varying answers. What is the answer when x = -3?</p>
<p>-3x^2 = ?</p>
<p>Logically and according to the principles my book gave it should be a positive number. There are no parentheses. It just says evaluate each polynomial for x = -3</p>
<p>So shouldn’t it be</p>
<p>-3 x the opposite of 3 x 3 = 27 , a positive number. I just don’t understand how the book is getting a negative number. Can anyone else cur, is the answer 27?</p>
<p>James thanks a lot bud I got it now. I just don’t know why the book didn’t say there are implied parentheses around variables next to constants. Does that also apply to variables next to variables? Am I stupid for not inferring this myself or is a common misconception to use the principles I did to get a positive number?</p>
<p>It’s not something that’s traditionally taught in books, but a lot of great teachers teach that concept because it makes problems a lot easier.</p>
<p>
</p>
<p>It can. xyz = (x)(y)(z)</p>
<p>
</p>
<p>I’d say a misconception. -3x^2 is always negative (except when x = 0) because the square of a number (+ or -) is always positive.</p>
<p>Remember PEMDAS - do exponents before multiplication. I’m adding a lot of parentheses here just to show where all of the signs go.</p>
<p>-3x^2 = (-3)<em>(x^2) and x=-3
so,
(-3)</em>(x^2) = (-3)<em>((-3)^2) = (-3)</em>(9) = -27</p>
<p>bcarvings think of this way</p>
<p>Here you have the problem -3x^2 right.</p>
<p>Now, you say that we assume that x is equal to -3 and we want to find the value of that expression. </p>
<p>Ok. Now if we put the expression into words, this is how it reads: Negative 3 multiplied by a number raised to the 2nd power. </p>
<p>Since we know the value of that number we can phrase it this way:</p>
<p>Negative 3 multiplied by negative 3 raised to the 2nd power</p>
<p>Notice that the ENTIRE quantity which is -3 here is being raised to the second power, meaning that you have to multiply -3 times -3 which is 9. </p>
<p>Basically since x ITSELF is being raised to the 2nd power, and if x IS -3 then -3 must also be raised to the second power.</p>
<p>This might also help understand:</p>
<p>-3² is -9 as well. If you have trouble understanding why, then just put it into words again.</p>
<p>Notice however that the above expression does not translate to -3 raised to the 2nd power, but instead translates to -1 multipled by 3 raised to the second power.</p>
<p>The quantity next to the power is always the one that is going to be affected by it</p>
<p>It was a bit long, but I hope it helped :P</p>
<p>eg very good explanation I really understand it now. If I didn’t have this site I might hire a part-time tutor and have to write all my questions down!</p>
<p>Thanks, its greatly appreciated!</p>