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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.

 Jan 25, 2020
 #1
avatar+18763 
+2

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?

 Jan 25, 2020
 #2
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-1

monic, this doesn't really help...

Guest Jan 25, 2020
 #3
avatar+108608 
0

Have you bothered to google what a monic polynomial is ?

 

Geno has answered your entire first question with full explaination and all you can say is "this doesn't really help"

 

What an ungracious person you are !!

Melody  Jan 25, 2020
 #4
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0

can someone help with the second one as well.

 Jan 27, 2020
 #5
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0

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

 Jan 28, 2020

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