Question

obtain a factor of y3-13y-12 factor theorem. hence factorize is completely

Answer 1

Let a be the factor of P(y), such that P(a) = 0. so that P(y-a) completely divides P(y). we know that the possible factors should be the factors of the constant term.

Hence the possible factor's are [ +-1,+-2,+-3,+-4,+-6]

using trial and error and putting a = -1, we see

P(-1) = -1³-13(-1)-12 = -1 +13 -12 = 0

Hence (y+1) will completely divide y³-13y-12

dividing both we get

(y³-13y-12)/(y+1) = y² -y -12

(y² -y -12) can be written as

=y² -4y + 3y -12

= y(y-4) + 3(y-4)

= (y+3)(y-4)

Hence,

(y³-13y-12) = (y+1)(y+3)(y-4)