SAT Math Problem Blue Book

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1

<p>Can anyone help me with the following math problem?</p>

<p>Test #3, Section 5, Problem #8:</p>

<p>(x-8)(x-k) = x² - 5kx + m</p>

<p>A) 8
B) 16
C) 24
D) 32
E) 40</p>

<p>Test #3, Section 8, Problem #14</p>

<p>Thank you--</p>

2

<p>Multiply the first two brackets to get :
x^2 -(k+8)x + 8k = x^2 - 5kx + m</p>

<p>Equate coefficient of x to find k :
k+8=5k
k=2</p>

<p>now equate constant terms
8k = m
8*2=m</p>

<p>m = 16.</p>

3

<p>I also had trouble with this at first.</p>

<p>If you’re familiar with FOIL, you’ll notice that m = (-8)(-k) and -5kx = (-xk + -8x)</p>

<p>You could then setup and equation: -xk -8x = -5kx which simplifies to -4kx = -8x</p>

<p>Since you know the equation is true for all values of x, plug in any number, like 1.</p>

<p>-4k = -8, k = 2</p>

<p>Since you know that m = (-8)(-k), you can substitute and get m=16</p>