## Intermediate Algebra (6th Edition)

$(x^2-2)(x^2-3)$
The two numbers whose product is $ac= 1(6)=6$ and whose sum is $b= -5$ are $\{ -2,-3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $x^4-5x^2+6$, is \begin{array}{l}\require{cancel} x^4-2x^2-3x^2+6 \\\\= (x^4-2x^2)-(3x^2-6) \\\\= x^2(x^2-2)-3(x^2-2) \\\\= (x^2-2)(x^2-3) .\end{array}