Sat practice Test #8 Answer Explanations

Choice D is correct. Since h (x) = 1 − g (x), substituting 0 for x yields
h (0) = 1 − g (0). Evaluating g (0) gives g (0) = 2(0) − 1 = −1. Therefore,
h (0) = 1 − (−1) = 2.
Choice A is incorrect. This choice may result from an arithmetic 
error. Choice B is incorrect. This choice may result from incorrectly 
evaluating g(0) to be 1. Choice C is incorrect. This choice may result 
from evaluating 1 − 0 instead of 1 − g(0).

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QUESTION 16
The correct answer is 3. The solution to the given equation can 
be found by factoring the quadratic expression. The factors can be 
determined by finding two numbers with a sum of 1 and a product 
of −12. The two numbers that meet these constraints are 4 and –3. 
Therefore, the given equation can be rewritten as (x + 4)(x − 3) = 0. It 
follows that the solutions to the equation are x = −4 or x = 3. Since it 
is given that a > 0, a must equal 3.
QUESTION 17
The correct answer is 32. The sum of the given expressions is 
(−2x 
2
+ x + 31) + (3x 
2
+ 7x − 8). Combining like terms yields x 
2
+ 8x + 23. 
Based on the form of the given equation, a = 1, b = 8, and c = 23. 
Therefore, a + b + c = 32.
Alternate approach: Because a + b + c is the value of ax 
2
+ bx + c when 
x = 1, it is possible to first make that substitution into each polynomial 
before adding them. When x = 1, the first polynomial is equal to
−2 + 1 + 31 = 30 and the second polynomial is equal to 3 + 7 − 8 = 2. 
The sum of 30 and 2 is 32.
QUESTION 18