<p>Ds2 is taking the SAT on Saturday and just finished a blue book test. The only math question he missed is:</p>
<p>If k and h are constants and x^2 + kx + 7 = (x+1)(x+h), what is the value of k?</p>
<p>Can anyone explain it? TIA</p>
<p>Foil the second expression: x^2 + hx + x + h.</p>
<p>Now combine like terms: x^2 + (h+1)x + h.</p>
<p>Because the original expression is x^2 + kx + 7, we know that h = 7 and (h+1) = (7+1) = k. So k = 8.</p>
<p>Thanks! That makes absolutely no sense to his liberal arts major mom, but I’m sure it will make perfect sense to him. :D</p>
<p>Daisie’s approach is correct. Perhaps it would help you and ds2 by taking a step back.</p>
<p>A basic theorem in algebra is that if two polynomials are equal for all values of x then the coefficients of like powers of x of the polynomials are equal.</p>
<p>A simple example is that of two linear equation (first degree polynomials in x)
ax + b = 2x - 3
where a and b are constants, and the equality holds for all values of x.
Then the theorem states that: a = 2, and b = -3</p>
<p>And similarly, another example for second degree polynomials:
ax^2 + bx + c = -3x^2 + 5x
where a, b and c are constants, and the equality holds for all values of x.
Then the theorem states that: a = -3, b = 5 and c = 0.</p>
<p>For this particular problem we have:
x^2 + kx + 7 = (x+1)(x+h)
Multiple out (x+1)(x+h) and you have:
x^2 + kx + 7 = x^2 + (h + 1) x + h
Now apply the theorem and you have h = 7 and k = 8.</p>
<p>If you’re unfamiliar with the theorem an alternate path to the answer is to “substitute” 2 values of x, as for example x = 0 and x = 1. You get two equations for k and h. Solve them.</p>