# SOLUTION: PLEASE PLEASE Factor 3x^3+11x^2+5x-3 using the factor theorem..... GOD BLESS WHO CAN HELP

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 Question 184750: PLEASE PLEASE Factor 3x^3+11x^2+5x-3 using the factor theorem..... GOD BLESS WHO CAN HELPAnswer by stanbon(57384)   (Show Source): You can put this solution on YOUR website!Factor 3x^3+11x^2+5x-3 using the factor theorem ------------- The easiest way to do these higher level polynomials (above quadratic) is to graph them to find the zeroes. ---------------- Using a graphing calculator, find there are zeroes at x = -3, x = -1, and 1/3 ------------------ So the factors are (x+3)(x+1) and (3x-1) ============================================ 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. --- 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. --- 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) --- By the Factor Th. the two remaining zeroes must be x = 1/3 and x = -3 ============================ Cheers, Stan H.