<p>1)when 4x^2+6x+L is divided by x+1, the remainder is 2. What is the value of L?</p>
<p>2)if f(x)= ((e^7x)+(square root 3))/2, and g(f(x))=x, then g(x)=?</p>
<p>3) A cube is inscribed in a sphere of radius 6. What is the volume of the cube?</p>
<ol>
<li>Use synthetic division and you are left with L-2 = -2 so L=4, sorry I wrote out how to do this before but it got deleted and I don’t feel like typing it again.</li>
<li>If g(f(x))= x, then g(x) is the inverse of f(x). This is the definition of an inverse. To find the inverse of f(x) switch f(x) and x in the equation then solve for f(x). Answer is
[ln(( 2x - (square root of 3))]/7, looks much more complicated than it is.</li>
<li>There is a simple formula for this type of question. If you know the diagonal of a cube you can find the side of a cube using the formula d= s(square root of 3). Solve for s which in this case is 6.93, then cube that number and the answer is 332.81</li>
</ol>
<p>The first one you can use Vietas if you know it.
For the second one, you can replug the answer choices back in, it seems like its an easier way to do it
3. This means the diagonal is 12, so use the formula above^</p>
<p>For number one the remainder theorem is the quickest way - you could use synthetic division but it would take longer. </p>
<p>The remainder is: If a polynomial is divided by x - a, then P(a) = the remainder, if its zero then x -a is a divisor.</p>
<p>thanks so much</p>
<p>Sportgreet03, isn’t the formula d = s(square root of 2) instead of s(square root of 3)??</p>
<p>Nope, the diagonal of a cube = s x sqrt(3)</p>