<p>This type of problem has arisen both times on two practice psat's i've taken. I took Alg 2, 2 years ago and have since forgotten most of these basic rules.</p>
<p>x^2 + kx + 4 = (x+c)^2</p>
<p>In the equation above, k and c are positive constants. If the equation is true for all values of x, what is the value of k?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32</p>
<p>Explanations. PLEASEE</p>
<p>this is a tricky one when you do NOT know how to do it. It is a very good question.</p>
<p>x^2 + kx + 4 = (x+c)^2</p>
<p>expand (x+c)^2 which is x^2 + 2xc + c^2</p>
<p>x^2 + kx + 4 = x^2 + 2xc + c^2</p>
<p>now then since they are equal you can assume that
x^2 = x^2
kx = 2xc
4 = c^2</p>
<p>so since we know
4 = c^2 so c = 2</p>
<p>x^2 + kx + 4 = x^2 + 4x + 4
since the equations are equal, kx = 4x which means k = 4 (B)</p>
<p>easy?</p>
<p>NICE! I never thought of that.</p>
<p>This might sound like a really stuipd and basic question but…</p>
<p>“expand (x+c)^2 which is x^2 + 2xc + c^2”
I understand how you got the X^2 and the C^2, but how did you get the 2XC by squaring the brackets?</p>
<p>@jeremy.
Multiply
(X<em>2)</em>(X<em>2) = X</em>X +2<em>X +2</em>X +2*2 =X^2 + 4X +4</p>
<p>oh umm… wow, I have done that so many times at school… I have no clue why I didn’t think about what (x+c)^2 ment.</p>
<p>-Duke
you multiplied within the parentheses where the values should be added, but the answer is the same</p>
<p>Wierd question.</p>