Review question

# Can we factorise $x^4 + Ax^2 + B$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7809

## Question

Suppose that the equation $x^4 + Ax^2 + B = (x^2 + ax + b)(x^2 - ax + b)$ holds for all values of $x$.

1. Find $A$ and $B$ in terms of $a$ and $b$.

2. Use this information to find a factorisation of the expression $x^4 - 20x^2 + 16$ as a product of two quadratics in $x$.

3. Show that the four solutions of the equation $x^4 - 20x^2 + 16 = 0$ can be written as $\pm \sqrt{7} \pm \sqrt{3}$.