SOLUTION: Factor. Check by using FOIL or the distributive property. m^3 + 6m^2 + 9m and then a question not from the book, b^2-6b-10, factor this one also please.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Factor. Check by using FOIL or the distributive property. m^3 + 6m^2 + 9m and then a question not from the book, b^2-6b-10, factor this one also please.      Log On


   



Question 37169This question is from textbook Algebra 1
: Factor. Check by using FOIL or the distributive property.
m^3 + 6m^2 + 9m
and then a question not from the book, b^2-6b-10, factor this one also please.
This question is from textbook Algebra 1

Found 2 solutions by josmiceli, jcmtnez:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
m%5E3+%2B+6%2Am%5E2+%2B+9%2Am
%28m%5E2+%2B+3%2Am%29%2A%28m+%2B+3%29
m%2A%28m+%2B+3%29%2A%28m+%2B+3%29
m%2A%28m%5E2+%2B6%2Am+%2B9%29
m%5E3+%2B+6%2Am%5E2+%2B+9%2Am
-------------------------
b%5E2+-+6%2Ab+-+10
complete the square
b%5E2+-+6%2Ab+%2B+3%5E2+=+10+%2B+3%5E2
%28b+-+3%29%5E2+=+19
take sqrt of both sides
b+-+3+=+%2B+sqrt%2819%29 (+ or - sqrt)
b+=+3+%2B+sqrt%2819%29
check by plugging b+=+3+%2B+sqrt%2819%29
and b+=+3+-+sqrt%2819%29
into b%5E2+-+6%2Ab+-+10
result should be zero
it checks for me

Answer by jcmtnez(53) About Me  (Show Source):
You can put this solution on YOUR website!
(1) Here is the first
m^3+6m^2+9m=0 , This polynomial of degree 3 is divisible by m, therefore we divede by m and get:
m(m^2+6m+9)=0 Now we have to solve the polynomial of degree two, and the solution is m=-3, and is unique. Finally we get
m(m+3)(m+3) As the factorization of m^3 + 6m^2 + 9m
(2) Here is the second
b^2-6b-10=0, First have to solve the equation, find the roots, we can do this using the general formula or using more advance methods. Using the formula we get as a result b=3+sqrt(19), and b=3-sqrt(19). Then the factors will be
(b-(3-sqrt(19))(b-(3+(sqrt(19))
b%5E2-6b-10=%28b-%283-sqrt%2819%29%29%29%28b-%283%2Bsqrt%2819%29%29%29