Question

question
factor completely over the integers.
$x^4 + 9x^2 + 20$

Explanation:

Step1: Let \( y = x^2 \)

Substitute \( y \) into the polynomial: \( y^2 + 9y + 20 \)

Step2: Factor the quadratic in \( y \)

Find two numbers that multiply to 20 and add to 9. The numbers are 4 and 5. So, \( y^2 + 9y + 20=(y + 4)(y + 5) \)

Step3: Substitute back \( y = x^2 \)

We get \( (x^2 + 4)(x^2 + 5) \). Both \( x^2 + 4 \) and \( x^2 + 5 \) cannot be factored over the integers further.

Answer:

\( (x^2 + 4)(x^2 + 5) \)