Digital PSAT Math Practice Question 167: Answer and Explanation
Question: 167
If the following equation is true for every value of x and if a is a constant, what is the value of a?
- A. -10
- B. -3
- C. -2
- D. 1
Correct Answer: B
Explanation:
(B) First, use FOIL for the left side of the equation:
Next, combine like terms:
We know that this has to equal the right side of the original equation:
The coefficients of the like terms on both sides of the equation must equal one another. The coefficients on the x3-terms are already equal and the constants are equal. So we need to worry about only the x2-terms and the x-terms. Set the coefficients on the x2-terms equal to one another:
Subtracting 4 from both sides reveals that a = -3, which is choice (B).
We also could have set the coefficients of the x-terms equal to each other to solve for a:
Subtracting 2 from both sides and then dividing by 4 gives a = -3 as well.
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