<p>1) If k and h are constants and x^2+kx+7 is equivalent to (x+1)(x+h), what is the value of k?</p>
<p>a 0
b 1
c 7
d 8
e It cannot be determined from the information given.</p>
<p>I searched everywhere but couldn't understand a step</p>
<p>(x +1)(x + h)
= x2 + hx + x + h
= x2 + (h +1)x + h --> How does the (H+1) appear?</p>
<p>hx and x are like terms. h is the coefficient of hx, 1 is the coefficient of x. By the combining like terms rule or whatever it’s called, you can combine them so hx + 1x = (h+1)x. You simply add the coefficients. And since x2 + (h+1)x + h = x2 + kx + 7 the coefficients of each expression must be equal, so h+1 = k and h = 7. Therefore k = 8.</p>
<p>When you multiply (x+1) * (x+h) you get x^2 + hx + x + h;
Now, you can combine terms 2 and 3 because they have the same power. The coefficient of term 2 is h and term 3 is 1;
Therefore, the coefficient of the resulting combined term will be (h+1);
The equation will ultimately be x^2 + (h+1)x + h;</p>
<p>Solving the rest of the equation:
We know that h = 7 because of the other equation;
Furthermore, we can deduce that h + 1 = k;
k, then is 7 + 1, or 8;</p>