Write $a^4 + 4$ as a product of two monic quadratics with integer coefficients.

Let me show you how to do the first one; maybe you can follow the procedure to do the second one.

Problem:             a⁴ + 4

Step 1 - complete the square; add and subtract that value:  (a⁴ + 4a² + 4) - 4a²

Step 2 - write as the difference of two squares:                        (a² + 2)² - (2a)²

Step 3 - factor:                                                               [ (a² + 2) - (2a) ] [  (a² + 2) + (2a) ]

Step 4 - remove the extra parentheses:                               (a² + 2 - 2a) (a² + 2 + 2a)

Step 5 - rewrite the terms (if you wish):                                (a² - 2a + 2) (a² + 2a + 2)  

Can you do the second problem?

can someone help with the second one as well.

What exactly do you need help with? You were provided with a full answer on how to do this!