One of the more difficult math problems in the Official SAT Study Guide 2nd Edition is on page 527 # 8
The Question:
(x-8)(x-k) = x²-5kx + m
In the question above, k and m are constants. If the equation is true for all values of x, what is the value of m?
The Solution:
Step 1 FOIL the left side so that x² -8x + 8k – kx = x² - 5kx + m
Step 2 add kx to both sides so x² -8x + 8k = x² -4kx + m
Step 3 subtract x² from both sides so -8x + 8K = -4kx + m
Step 4 we know that -8x must equal – 4kx so solve for k as follows:
Divide both sides by x so -8 = -4k; k=2
Step 5 we also know that 8k = m; so 8 (2) = 16; choice B
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