<p>Hey, help please</p>
<p>(X-8)(X-K)=X^2-5KX+m
In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?</p>
<p>m= (4k-8)x + 8k.</p>
<p>In problems like this you just want to try to move around the terms so the variable you’re solving for is alone on its side of the = sign.</p>
<p>Here it is step by step.</p>
<p>FOIL the left side to get
x^2-8x-kx+8k=x^2-5kx+m
subtract x^2 from both sides to get
-8x-kx+8k=-5kx+m
add 5kx to both sides to get
-8x+4kx+8k=m
factor out an x and it simplifies to
x(-8+4k)+8k=m</p>
<p>um, thank you, but actually they were looking for a number that equals these
a- 8
b- 16
c- 24
d- 32
e- 40</p>
<p>Then you havent provided a full text of the problem. What does k and x equal to?</p>
<p>So, m= (4k-8)x + 8k.
From here what you can do is just assume different values for x
Let’s say x=0
then,
m=8k eqn(i)</p>
<p>This time let’s assume a=1
then we have,
m=4k-8+8k
m=12k-8 eqn(ii)
Solving eqn(i) and eqn(ii) you’ll get
m=16 and k=2</p>
<p>So, the answer is b.</p>
<p>from knowing how to foil you know that</p>
<p>(-8)(-k) = m</p>
<p>and</p>
<p>(-8)+(-k) = -5k</p>
<p>so you can plug in for m and see if its true</p>
<p>m=16
(-8)(-k)=16
k=2</p>
<p>(-8)+(-2) = (-5)(2)
-10=-10</p>
<p>if you try the other choices for m it doesn’t work. not sure if this method is faster or better, but it works.</p>