<p>if (x+2)^n (x-2) = (x+2) (x^2 -4) for all value of x, what is the value of n? </p>
<p>a)1
b)2
c)3
d)4
e) it cannot be determined from the information given.</p>
<p>Ans is B</p>
<p>....................
Is there a fast way to solve instead of plugging choices and simply multiplying to compare both sides of the equation? </p>
<p>Yes! There are actually 2 ways
The first one: (x+2)^(n-1) = (x^2-4)/(x-2)
<=>(x+2)^(n-1) = (x-2)(x+2)/(x-2)
<=>(x+2)^(n-1) = x+2
<=>n-1 = 1
<=>n = 2</p>
<p>The second one is more practical and faster
When they say “for all value of x”, plug in x=0
x=0 <=> 2^n . (-2) = 2.(-4)
<=> 2^n = 4
<=> n = 2</p>
<p>OMG ! Thank you so much ! So Helpful </p>
<p>Another way to approach it is by looking at the right side. (x+2) (x^2 -4) factors to (x+2) (x+2)(x-2). This is simply the sum and difference product rule.</p>
<p><a href=“Box”>https://app.box.com/s/5lq25lhegnhno6e8ujgl</a> please help with section 2. numbers 8 14 and 18. also please help with 15 and 16 because I feel like my answers are correct but the answer key says it’s not. I got 22 and 4.9 for 15 and 16. thank you</p>
<p>@sat2014 please start your own thread next time
8. C
first team will play 6 games, second team will play 4 additional games (exclude overlap), third team will play 2 additional games, last team has been covered. That’s 12 teams. alternatively you can list them
AB, AC, AD, BC, BD, CD that’s six, multiply by two.</p>
<ol>
<li><p>5000
y= .125x+55000
initial x=210000
final x=250000
plug in initial = .125(210000)+55000
plug in final = .125(250000)+55000
do final - initial = 5000</p></li>
<li><p>42
adding the side lengths across the bottom root(36)+root(25)+root1= 6+5+1=12
adding the side lengths vertical gives you root(36)+root(16)=6+4=10
10*12=120 for the rectangle
add 16+36+25+1= 78
120-78= 42</p></li>
<li><p>5<x<6 (x-1)(x-r)<0="" when="" x=“5” (x-1)(x-r)="">0 when x=6
4(5-r)<0 5(6-r)>0
5-5= 0 and 6-6=0, so the first will be less than 0 for any number greater than 5, the second will be less than 0 for any number less than 6
so any number between 5 and 6 will work </x<6></p></li>
<li><p>4/3
x^2+y^2= 25
you know that x=-4 and it is on the circle
so 4^2+y^2=25
y^2=25-16=9
y=3
a line from (0,0) to (-4,3) would be perpendicular to the line because a tangent line is perpendicular to the circle.
that has a slope of -3/4 to find perpendicular slope take the negative reciprocal, 4/3</p></li>
</ol>
<p>@guineagirl96 Thank You</p>