Question

Which of the following is a factor of \( x^4 + 4x^2 + 3 \)?

• A. \( x^2 - 1 \)
• B. \( x^2 + 3 \)
• C. \( x^2 - 3 \)
• D. None of these

Hint:

When factoring higher-degree polynomials, try breaking them down into smaller quadratic factors by looking for patterns.

Answer 1

The Correct Option is B

We are given the expression \( x^4 + 4x^2 + 3 \). Let's check if any of the options are factors of this expression.
Let's first factor \( x^4 + 4x^2 + 3 \): \[ x^4 + 4x^2 + 3 = (x^2 + 3)(x^2 + 1) \] Thus, \( x^2 + 3 \) is a factor of the given expression. Therefore, the correct answer is \( x^2 + 3 \).