Honestly Do NOT understand this Math problem. Help?

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1

<p>I have the second edition Blue book and I’m currently working on my math. I saving the first three tests like everyone always say so I'm starting with the last test in the book and its on page 969 if you have the book, problem 17.</p>

<p>If you don't well here it is:</p>

<p>If k and h are constants and x-squared + kx + 7 is equivalent to (x+1) (x+h), what is the value of K? </p>

<p>(P.S- I can't find a way to write x- squared on here so just imagined a little exponential 2 on top of the x)</p>

<p>A- 0
B-1
C-7
D-8
E- Not enough info given to determine</p>

<p>I know the answer is D but I could care less, I just want to know how to get the answer. I looked at the explanations that CB gives but its making no sense to me</p>

2

<p>Did you try FOIL-ing (x+1)(x+h)? You’ll get x^2 + (h+1)x + h … How can this equal x^2 + kx + 7 for every possible x value? Only if h = 7 and (h+1) = k. Hope this helps…</p>

3

<p>So you know
x^2 + kx + 7 = (x+1)(x+h)</p>

<p>You don’t even need to worry about the right side. Since 7 is prime, it only has 2 factors, 1 and 7. That means the factors of the left side must be
(x+7)(x+1)</p>

<p>Now multiply that out:
x^2 + 8x + 7</p>

<p>k = 8.</p>

4

<p>@fignewton and H3XH3X- I know that I need to foil but when I take (x +1) (x +h) and foil it to x^2 + x + hx + h, I don’t see how that turns into x^2 + (h+1)x + h</p>

<p>Sorry to ask so much but a little bit more explination should do the trick :)</p>

5

<p>X=1x, so if you factor hx+x, you get (h+1)x.</p>

6

<p>Above solutions are all fine. But this one also works if you make up numbers…</p>

<p>x^2 + kx + 7 = (x+1)(x+h)</p>

<p>has to be true for all x. So say we try x = 0…</p>

<p>0 + 0 + 7 = (1)(h) and now we know h = 7.</p>

<p>Now try x = 1…</p>

<p>1^2 + k + 7 = (1+1)(1 + 7)
k + 8 = 16
k = 8</p>

<p>Or, if you like this approach and you have a moment of inspired laziness:</p>

<p>Start again, this time with x = -1 …</p>

<p>x^2 + kx + 7 = (x+1)(x+h)</p>

<p>1 + (-k) + 7 = 0</p>

<p>k = 8</p>

<p>That’s my favorite method (but I didn’t try -1 until after I had already used 0 and 1…I’ll try to be lazier more quickly next time.)</p>

7

<p>Just use the FOIL method backwards. Since you know that the last term is 7, and you also know that it is a prime number, you should be able to figure out that the equation is:</p>

<p>(x+1)(x+7)</p>

<p>So then, all you have to do if FOIL that and end up with this:</p>

<p>x^2+8x+7</p>

<p>So therefore, K = 8.</p>