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.