# SOLUTION: Question: Factor: 2x^4-5x^3-10x^2+15x+18 (a) (2x-3) (x+1) (x+2) (x-3) (b) 2x+3) (x-1) (x-2) (x+3) (c) (2x+3) (x+1) (x-2) (x-3) (d) (2x-3) (x-1) (x+2) (x+3) Thank you

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: Question: Factor: 2x^4-5x^3-10x^2+15x+18 (a) (2x-3) (x+1) (x+2) (x-3) (b) 2x+3) (x-1) (x-2) (x+3) (c) (2x+3) (x+1) (x-2) (x-3) (d) (2x-3) (x-1) (x+2) (x+3) Thank you      Log On

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 Click here to see ALL problems on Linear Algebra Question 30354: Question: Factor: 2x^4-5x^3-10x^2+15x+18 (a) (2x-3) (x+1) (x+2) (x-3) (b) 2x+3) (x-1) (x-2) (x+3) (c) (2x+3) (x+1) (x-2) (x-3) (d) (2x-3) (x-1) (x+2) (x+3) Thank youAnswer by sdmmadam@yahoo.com(530)   (Show Source): You can put this solution on YOUR website!Let f(x) = 2x^4-5x^3-10x^2+15x+18 = 0 Trying values by inspection x = -1, 2 ,3 and (-3/2) hold Therefore [x-(-1)], (x-2), (x-3) and (2x+3) are the factors Hence 2x^4-5x^3-10x^2+15x+18 = (2x+3) (x+1) (x-2) (x-3) Therefore choice (c) (2x+3) (x+1) (x-2) (x-3) is correct Remark: So much is the answer if the question is a 1 mark - marking the right answer question. If it carries more marks, then the steps are By inspection x = -1 is a root of f(x) = 0 This means (x+1) is a factor On long division of (2x^4-5x^3-10x^2+15x+18 ) by (x+1) You get (2x^3-7x^2-3x+18)=g(x) say By inspection x = 2 is a root of g(x) = 0 This means (x-2) is a factor On long division of (2x^3-7x^2-3x+18)by (x-2) you get (2x^2-3x-9) And (2x^2-3x-9)= (x-3)(2x+3) Therefore 2x^4-5x^3-10x^2+15x+18 = (2x+3) (x+1) (x-2) (x-3) which is choice (c)