2020 · Q35
What is the square root of 4x⁴ + 8x³ − 4x + 1?
Elementary MathematicsAlgebra
- A2x² − 2x − 1
- B2x² − x − 1
- C2x² + 2x + 1
- D2x² + 2x − 1
Explanation
Expanding (2x^2+2x-1)^2 gives 4x^4+8x^3-4x+1 exactly, so the square root is 2x^2+2x-1 - option (D).The other options fail: for example (2x^2+2x+1)^2 produces a +4x^2 term that cannot cancel. Matching the x^3 and x coefficients uniquely picks 2x^2+2x-1.