SOLUTION: https://gyazo.com/5564d9bf43770b396a007976c63f945a

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Question 1177784: https://gyazo.com/5564d9bf43770b396a007976c63f945a
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if f%28-3%29=0 we know one root is x%5B1%5D=-3
using the product rule, we know that %28x-%28-3%29%29=%28x%2B3%29 will be one factor and
f%28x%29=8x%5E3%2B74x%5E2%2B200x%2B150 will be divisible by %28x%2B3%29
using long division or calculator, we get
%288+x%5E3+%2B+74+x%5E2+%2B+200+x+%2B+150%29%2F%28x+%2B+3%29=8+x%5E2+%2B+50+x+%2B+50

so, factor 8+x%5E2+%2B+50+x+%2B+50+
2%28+4x%5E2+%2B+25x+%2B+25%29+
2%28+4x%5E2+%2B+20x%2B5x+%2B+25%29+
2%28+%284x%5E2+%2B+20x%29%2B%285x+%2B+25%29%29+
2%284x+%28x+%2B+5%29%2B5%28x+%2B+5%29%29+
2+%28x+%2B+5%29+%284x+%2B+5%29+
other factors are 2+%28x+%2B+5%29+%284x+%2B+5%29+
and
8+x%5E3+%2B+74+x%5E2+%2B+200+x+%2B+150+=+2+%28x+%2B+5%29+%284x+%2B+5%29+%28x+%2B+3%29+