SOLUTION: f(x)=15x^3+61x^2+2x-8 List all possible rational zeros Find all rational zeros Factor f(x)

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Question 1000694: f(x)=15x^3+61x^2+2x-8
List all possible rational zeros
Find all rational zeros
Factor f(x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=15x%5E3%2B61x%5E2%2B2x-8
to find all possible rational zeros, set f%28x%29=0
15x%5E3%2B61x%5E2%2B2x-8=0.........factor completely
15x%5E3%2B6x%5E2%2B55x%5E2%2B22x-20x-8=0.....group
%2815x%5E3%2B6x%5E2%29%2B%2855x%5E2%2B22x%29-%2820x%2B8%29=0
3x%5E2%285x%2B2%29%2B11x%285x%2B2%29-4%285x%2B2%29=0
%283x%5E2%2B11x-4%29%285x%2B2%29+=+0
%283x%5E2-x%2B12x-4%29%285x%2B2%29+=+0
%28%283x%5E2-x%29%2B%2812x-4%29%29%285x%2B2%29+=+0
%28x%283x-1%29%2B4%283x-1%29%29%285x%2B2%29+=+0
%28x%2B4%29%283x-1%29%285x%2B2%29+=+0

solutions:
if %28x%2B4%29+=+0=>highlight%28x=-4%29
if %283x-1%29+=+0=>3x=1=>highlight%28x=1%2F3%29
if %285x%2B2%29+=+0=>5x=-2=>highlight%28x=-2%2F5%29