Advanced MathVery hardConstant from a partial-fraction style identity
Advanced Math practice question
For x ≠ 2, the expression (x² − 4)/(x − 2) + k is equal to x + 7 for every such x, where k is a constant. What is the value of k?
Answer: 5
(x² − 4)/(x − 2) = (x − 2)(x + 2)/(x − 2) = x + 2. So x + 2 + k = x + 7 and k = 5.
Common wrong answers
- If you answered 3
- 3 would give x + 5, not x + 7; the fraction simplifies to x + 2, so k must be 5.
- If you answered 7
- 7 forgets that the fraction already simplifies to x + 2, not x.
- If you answered -5
- −5 has the wrong sign.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.