For the polynomial below, 3 is a zero.
f(x)= 3x^3 - 10x^2 + x + 6
Express f(x) as a product of linear factors.
Use fractions or square roots, not decimals.
Test: f(3) = 81-90+3+6=0.
f(x) = 3x^3 - 10x^2 + x + 6 = 3x^2(x-3) + 9x^2 - 10x^2 + x + 6 = 3x^2(x-3) - x^2 + x + 6 = 3x^2(x-3) - x(x-3) - 3x + x + 6 = 3x^2(x-3) - x(x-3) - 2x + 6 = 3x^2(x-3) - x(x-3) - 2(x-3) =(x-3)(3x^2-x-2).
Now solve the quadratic equation (3x^2-x-2)=0,x1,2 = (1+-sqrt(25))/6 = 1 and -2/3.
The answer: f(x) = (x-3)(x-1)(3x+2). ( 3x+2 is 3*(x+2/3) )
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