Simplify the following polynomial and find the leading term: \(3x^4 - 5x^3 + 2x^2 - 3x + 1 - (2x^4 + x^3 - x^2 + 2x -1)\)
Simplify each term: \(x^4 - 6x^3 + 3x^2 - 5x + 2\)
Step 1 :First, distribute the negative sign to each term inside the parentheses: \(3x^4 - 5x^3 + 2x^2 - 3x + 1 - 2x^4 - x^3 + x^2 - 2x +1\)
Step 2 :Then, combine like terms: \((3x^4 - 2x^4) + (-5x^3 - x^3) + (2x^2 + x^2) + (-3x - 2x) + (1 + 1)\)
Step 3 :Simplify each term: \(x^4 - 6x^3 + 3x^2 - 5x + 2\)