### Reformatting the intake :

Changes do to her input should not influence the solution: (1): "x2" was replaced by "x^2". 1 an ext similar replacement(s).

You are watching: Factor the polynomial. 3x3 – 12x2 + 27x

## Step 1 :

Equation in ~ the finish of action 1 :

((3 • (x3)) - (22•3x2)) + 27x

## action 2 :

Equation in ~ the finish of step 2 : (3x3 - (22•3x2)) + 27x

## Step 4 :

Pulling out like terms :4.1 pull out like factors:3x3 - 12x2 + 27x=3x•(x2 - 4x + 9)

Trying to factor by dividing the center term

4.2Factoring x2 - 4x + 9 The first term is, x2 its coefficient is 1.The middle term is, -4x the coefficient is -4.The critical term, "the constant", is +9Step-1 : multiply the coefficient of the very first term by the continuous 1•9=9Step-2 : find two determinants of 9 whose sum equals the coefficient that the center term, which is -4.

 -9 + -1 = -10 -3 + -3 = -6 -1 + -9 = -10 1 + 9 = 10 3 + 3 = 6 9 + 1 = 10

Observation : No 2 such components can be found !! Conclusion : Trinomial can not it is in factored

## Final result :

3x • (x2 - 4x + 9)

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