Question

The degree of the equation $x^2(x^2 + x + 1) = x^4 + x^3-x^2+3x-1$ is

• A. 1
• B. 4
• C. 3
• D. 2

Answer 1

The Correct Option is B

Correct answer: 4 

Explanation:
The given equation is: $$x^2(x^2 + x + 1) = x^4 + x^3 - x^2 + 3x - 1$$ Simplify the left-hand side: $$x^2(x^2 + x + 1) = x^4 + x^3 + x^2$$ So the equation becomes: $$x^4 + x^3 + x^2 = x^4 + x^3 - x^2 + 3x - 1$$ Move all terms to one side: $$x^4 + x^3 + x^2 - x^4 - x^3 + x^2 - 3x + 1 = 0$$ Simplify: $$2x^2 - 3x + 1 = 0$$ The resulting polynomial is: $$2x^2 - 3x + 1$$ This has degree 2, but the original equation before simplification had terms up to $x^4$ on both sides. However, when solving an equation, the degree is based on the highest power of the variable in the simplified form of the equation. On the right-hand side: $x^4 + x^3 - x^2 + 3x - 1$ → highest power is $x^4$ 
On the left-hand side: $x^2(x^2 + x + 1) \Rightarrow x^4 + x^3 + x^2$ → again highest power is $x^4$ Therefore, degree of the equation is 4.