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 you
Answer 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)
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