SOLUTION: For the function f(x) = 12x^3 - 28x^2 + 7x + 12 ; List all possible rational zeros, find all zeros, and list all factors.

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Question 472569: For the function
f(x) = 12x^3 - 28x^2 + 7x + 12 ;
List all possible rational zeros, find all zeros, and list all factors.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+12x%5E3+-+28x%5E2+%2B+7x+%2B+12+....replace -+28x%5E2 with -+10x%5E2-+18x%5E2 and 7x with 15x-8x

f%28x%29=12x%5E3-10x%5E2-18x%5E2%2B15x-8x%2B12......group

f%28x%29=%2812x%5E3-18x%5E2%29-%2810x%5E2-15x%29-%288x-12%29

f%28x%29=6x%5E2%282x-3%29-5x%282x-3%29-4%282x-3%29

f%28x%29=%286x%5E2-5x-4%29%282x-3%29........replace -5x with -8x%2B3x

f%28x%29=%286x%5E2%2B3x-8x-4%29%282x-3%29.....group

f%28x%29=%28%286x%5E2%2B3x%29-%288x%2B4%29%29%282x-3%29

f%28x%29=%283x%282x%2B1%29-4%282x%2B1%29%29%282x-3%29

f%28x%29=%283x-4%29%282x%2B1%29%29%282x-3%29

now when we have factored it we can set each factor of this product to zero and find solutions:

if 3x-4=0...->...3x=4...->..x=4%2F3
if 2x%2B1=0...->...2x=-1...->..x=-1%2F2
if 2x-3=0...->...2x=3...->..x=3%2F2