bearing in mind that, the geometric sequence is "convergent" only when |r|<1, or namely "r" is a fraction between 0 and 1.
7. Given the systems below, state how many solutions there are. YOU MUST GIVE A REASON
1 answer:
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bearing in mind that, the geometric sequence is "convergent" only when |r|<1, or namely "r" is a fraction between 0 and 1.
We are dividing the polynomial 
by x+4
notice that
is x times 2x,
so if we multiply (x+4) by 2x, which gives us
, we can 'separate' one from to get the following simplification:
similarly we notice that 5x is x times 5, so if we multiply (x+4) by 5, we get 5x+20 so we can rewrite
can not be simplified any further since the degree of 6, is smaller than the degree of x+4
combining our work, we have:
Answer:
q(x)= 2x+5
r(x)=6
b(x)=x+4
Remark: we can solve the problem by long division or the division algorithm as well.
notice that
so if we multiply (x+4) by 2x, which gives us
similarly we notice that 5x is x times 5, so if we multiply (x+4) by 5, we get 5x+20 so we can rewrite
combining our work, we have:
Answer:
q(x)= 2x+5
r(x)=6
b(x)=x+4
Remark: we can solve the problem by long division or the division algorithm as well.