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

Write $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients.

Guest Jan 25, 2020

#1**+2 **

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

Problem: a^{4} + 4

Step 1 - complete the square; add and subtract that value: (a^{4} + 4a^{2} + 4) - 4a^{2}

Step 2 - write as the difference of two squares: (a^{2} + 2)^{2} - (2a)^{2}

Step 3 - factor: [ (a^{2} + 2) - (2a) ] [ (a^{2} + 2) + (2a) ]

Step 4 - remove the extra parentheses: (a^{2} + 2 - 2a) (a^{2} + 2 + 2a)

Step 5 - rewrite the terms (if you wish): (a^{2} - 2a + 2) (a^{2} + 2a + 2)

Can you do the second problem?

geno3141 Jan 25, 2020