Write polynomial P as a product of linear factors : P(x) = 5x^3 -2x^2 + 5x - 2

Given the polynomial P(x) = 5x^3 - 2x^2 + 5x
-2

We need to factor
P(x).

First we will rearrange the terms of
P(x).

==> P(x) = 5x^3 + 5x - 2x^2 -
2

Now we will factor 5x from the first two
terms.

==> P(x) = 5x (x^2 +1) - 2x^2
-2

Now we will factor -2 from the last two
terms.

==> P(x) = 5x(x^2 +1) -2 ( x^2 +
1)

Now we will factor
(x^2+1).

==> P(x) = (x^2 + 1)
(5x-2)

Now we will factor (x^2
+1)

==> P(x) = (x-i)(x+i) (
5x-2)

 

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