Question 1177784

if {{{f(-3)=0}}} we know one root is {{{x[1]=-3}}}

using the product rule, we know that {{{(x-(-3))=(x+3)}}} will be one factor and 

{{{f(x)=8x^3+74x^2+200x+150}}} will be divisible by {{{(x+3)}}}

using long division or calculator, we get

{{{(8 x^3 + 74 x^2 + 200 x + 150)/(x + 3)=8 x^2 + 50 x + 50}}}


so, factor  {{{8 x^2 + 50 x + 50 }}}

{{{2( 4x^2 + 25x + 25) }}}

{{{2( 4x^2 + 20x+5x + 25) }}}

{{{2( (4x^2 + 20x)+(5x + 25)) }}}

{{{2(4x (x + 5)+5(x + 5)) }}}

{{{2 (x + 5) (4x + 5) }}}

other factors are {{{2 (x + 5) (4x + 5) }}}

and

{{{8 x^3 + 74 x^2 + 200 x + 150 = 2 (x + 5) (4x + 5) (x + 3) }}}