<p>If x>0, n is a nonnegative integer, and 2x^(n+1) + x^(n+2) = x^(n+3), which of the following must equal x^3?</p>
<p>a) 2+2x+x^2
b) 2x+x^2
c) 2+x^2
d) 2+x
e) 3x</p>
<p>Kudos to whoever solves it.</p>
<p>Just let n = 0, substitute.</p>
<p>2x^(0+1) + x^(0+2) = x^(0+3)</p>
<p>2x + x^2 = x^3, answer choice B.</p>
<p>That wasn’t impossible, was it?</p>
<p>Wow. I’ve spent 45 minutes trying to solve this question. Can you show me the mathematic way of solving it? Like using substitution and such.</p>
<p>Yeah, just substitute “n” with “0” and simplify (see my post above).</p>
<p>Here is one way to solve it: If 2x^(n+1)+x^(n+2)=x^(n+3), collecting terms on one side
x^(n+3)-x^(n+2)-2x^(n+1)=0, factoring out x^n we have (x^n)(x^3-x^2-2x)=0. x^n can not be zero so we can divide by that, leaving x^3-x^2-2x=0. Solving for x^3, we have x^3=x^2+2x which is B.</p>
<p>That wasn’t so hard, was it?</p>
<p>You guys are great, thank you!</p>
<p>
You want to write the exponents in the form 2(x^n)(x^1) + (x^n)(x^2) = (x^n)(x^3), at which point you can see that (x^n) can be factored out. Then you have 2(x^1) + (x^2) = (x^3).</p>
<p>The answer is B) </p>
<p>2x^n+1 + x^n+2 = x^n+3<br>
x^n * ( 2x+x² ) = x^n * x^3
You divide by x^n :
2x+x2 = x^3</p>