Ecpress g(x) as a product of linear factors from a polynomial

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For the polynomial below, -2 is a zero.

g(x)= x^3 - 2x^2 - 9x - 2

Express g(x) as a product of linear factors.

Oct 25th, 2015

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x = -2 is a zero of g(x).

So x + 2 is a factor of g(x).

Divide g(x) by (x + 2 ) to find the other factors


So



Now factor  using the quadratic formula so that g(x) can be expressed as a product of linear factors.

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Oct 25th, 2015

a = 1, b = -4 , c = -1

The quadratic formula is


Oct 25th, 2015

Substitute values of a,b and c in the formula.


Oct 25th, 2015

So  and  are the zeros of the equation  .


Oct 25th, 2015


Oct 25th, 2015


So

Oct 25th, 2015


expresses g(x) as a product of linear factors.

Oct 25th, 2015

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