SOLUTION: factor: 2x^5 + x^4 - 8x^3 - 4x^2

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 209557: factor: 2x^5 + x^4 - 8x^3 - 4x^2Found 3 solutions by stanbon, nerdybill, MathTherapy:Answer by stanbon(57361)   (Show Source): You can put this solution on YOUR website!factor: 2x^5 + x^4 - 8x^3 - 4x^2 ---- x^2(2x^3 + x^2 - 8x - 4) --- I graphed the cubic and found a zero at x = 2 Then using synthetic division I got: 2)....2.....1.....-8.....-4 .......2.....5......2....|..0 Quotient: 2x^2+5x+2 = (2x+1)(x+2) = x^2(2x+1)(x-2)(x+2) ============================== Cheers, Stan H. Reply to stanbon@comcast.net Answer by nerdybill(6962)   (Show Source): You can put this solution on YOUR website!factor: 2x^5 + x^4 - 8x^3 - 4x^2 . Begin by factoring out what is common among all terms: x[2x^4 + x^3 - 8x^2 - 4x] . Group terms: x[(2x^4 + x^3) - (8x^2 + 4x)] . Factor expressions inside parentheses: x[x^3(2x + 1) - 4x(2x + 1)] x[(2x + 1)(x^3- 4x)] x(2x + 1)(x^3- 4x) Answer by MathTherapy(1425)   (Show Source): You can put this solution on YOUR website! ------ Factor out GCF, ------ Factor the inner polynomial Therefore, we have: Factor to get: