Advanced MathVery hardFactoring a difference of fourth powers
Advanced Math practice question
Which expression is equivalent to (x⁴ − 16)/(x² + 4) for all values of x?
- A. x² − 4Correct
- B. x² + 4
- C. x − 2
- D. x⁴ − 4
Answer: A. x² − 4
x⁴ − 16 = (x² + 4)(x² − 4), and the x² + 4 cancels.
Why the other answers are wrong
- B. x² + 4
- This keeps the wrong factor.
- C. x − 2
- x² − 4 factors further but does not reduce to x − 2 here.
- D. x⁴ − 4
- Division does not subtract the constants.
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.