Question 184750: PLEASE PLEASE
Factor 3x^3+11x^2+5x-3 using the factor theorem..... GOD BLESS WHO CAN HELP
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Factor 3x^3+11x^2+5x-3 using the factor theorem
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The easiest way to do these higher level polynomials (above quadratic)
is to graph them to find the zeroes.
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Using a graphing calculator, find there are zeroes at x = -3, x = -1, and 1/3
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So the factors are (x+3)(x+1) and (3x-1)
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If you are not allowed to use a calculator you know any rational roots
of the form p/q must have p as a factor of -3 and q as a factor of 3.
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So you would check 1,-1,3,-1,1/3,-1/3 , using synthetic division:
Since the coefficents do not add up to zero you know 1 is not a zero.
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Checking x = -1 you get:
-1)....3....11......5....-3
........3....8.....-3...|..0
Quotient = 3x^2 + 8x -3
which factors as (3x-1)(x+3)
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By the Factor Th. the two remaining zeroes must be x = 1/3 and x = -3
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Cheers,
Stan H.
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