<p>At how many points do the graphs of x^2 + y^2 = 9 and xy=3 intersect? 0, 1, 2, 3, 4? </p>
<p>If 2x+4 is a factor of 2x^3 + 4x^2 + d, then d could equal? 42, 28, 22, 8, 2</p>
<p>What is the center for the circle represented by the equation x^2+y^2-4x+2y-4=0? </p>
<p>-2, -4
-1,4
0,-1
2,-1
4,2</p>
<ol>
<li>4</li>
<li>No solution (unless I'm mistaken)</li>
<li>(2, -1)</li>
</ol>
<p>I think #2 is 42. It can't be no solution, because that's not an answer choice. I just plugged in x = 1, which gave me:</p>
<p>2x + 4: 2(1) + 4 = 6</p>
<p>2x^3 + 4x^2 + d: 2(1)^3 + 4(1)^2 + d = 24 + d</p>
<p>Obviously 6 can only be a factor of 24 + d is d is some multiple of six. The only answer choice that satisfies that is 42.</p>
<p>I agree with Differentiable on #1 and #3, though.</p>
<p>The problem is that 2x+4 is not a factor of 2x^3 + 4x^2 + 42.</p>
<p>Because none of the answers fit, I assume that the question was copied incorrectly.</p>
<p>all the questions were coppied correctly.</p>
<p>then there must be an error, because none of those answer choices can be correct.</p>
<p>d=0 </p>
<p>(2x+4)(x^2+ax+b)=2x^3+(4+2a)x^2+(4a+2b)x+4b</p>
<p>2x^3+(4+2a)x^2+(4a+2b)x+4b=2x^3+4x^2+d</p>
<p>4+2a=4
a=0</p>
<p>4a+2b=0
b=0</p>
<p>4b=0=d</p>
<p>yeah that's what i got too, but that's not one of the answer choices.</p>
<ol>
<li>I agree with Differential & Johnny182. If (2x+4) is a factor, then
(2x+4)(x^2 + bx + c) = 2x^3 + 4x^2 + d
or
2x^3 + (4+2b)x^2 + (4b+2c)x + 4c = 2x^3 + 4x^2 + d</li>
</ol>
<p>so (4+2b) = 4, or b=0
and (4b+2c) = 0 , or c=0
and (4c) = d, from which d must = 0.</p>
<p>I suspect whoever solved it did it like Zach447 did, plugging in x=1. If you plug in (say) x=2, you get a different & conflicting answer. You need a value for d that's kosher for <em>all</em> x values.</p>
<p>gameguy88,
Where are the problems from? If you copied them correctly, then your practice problem source is not very reliable.</p>