Rewrite the expression g^4 + 18g^2 + 24 in the form c(g^2 + p)^2 + q. What is q?

Guest May 18, 2021

#1**+1 **

\(c(g^2+p)^2+q\\=c(g^4+2g^2p+p^2)+q\\=cg^4+2cg^2p+p^2c+q\)

Set up system of equation according to corresponding coefficients:

\(c=1\\ 2cp=18\\ p^2c+q=24\\ \)

Substitute first equation to second:

\(2(1)p=18\\p=9\)

Lastly, substitute first and second equation to third equation:

\(9^2(1)+q=24\\q=\boxed{-57}\)

I hope this helps (❁´◡`❁)

ok bye

randomMember May 18, 2021

#1**+1 **

Best Answer

\(c(g^2+p)^2+q\\=c(g^4+2g^2p+p^2)+q\\=cg^4+2cg^2p+p^2c+q\)

Set up system of equation according to corresponding coefficients:

\(c=1\\ 2cp=18\\ p^2c+q=24\\ \)

Substitute first equation to second:

\(2(1)p=18\\p=9\)

Lastly, substitute first and second equation to third equation:

\(9^2(1)+q=24\\q=\boxed{-57}\)

I hope this helps (❁´◡`❁)

ok bye

randomMember May 18, 2021