What is the answer to 4s5+8s4+5s3+10s2? Factor it

1 Answer
Apr 9, 2018

Please look below.

Explanation:

f(s)=4s5+8s4+5s3+10s2
f(s)=s2(4s3+8s2+5s+10)

After factoring out s2 we are left with a polynomial of degree 3 to factorise g(s)=4s3+8s2+5s+10. This can be done using the factor theorem.

After testing some integers it can be found that:
g(2)=0

Hence (s+2) is a factor of g(s) and can be factored out by long division. This gives the result:
g(s)=(s+2)(4s2+5)

4s2+5 can be factorised further using the quadratic formula.
s=0±024×4×52×4
s=±808
s=±i52

Hence
g(s)=(s+2)(s+i52)(si52)

And to answer your question:
4s5+8s4+5s3+10s2=s2(s+2)(s+i52)(si52)