Express the polynomial as a product of linear factors f (x) = x3-5x2-18x+72

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Mathematics

Devon

8 October, 19:11

Express the polynomial as a product of linear factors f (x) = x3-5x2-18x+72

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Mike Summers · Answer 1

Try out some factors of 72 to see which are roots of f (x).

f (3) = 27 - 45 - 54 + 72 = 0 and f (-3) = - 27 - 45 + 54 + 72 = 54,

so 3 is a root and - 3 is not. For confirmation, we have f (-4) = 0

and f (6) = 0, so (x - 3) (x + 4) (x - 6)