What is factor 27x^3-135x^2+225x-125 ?

The solution to factor 27x^3-135x^2+225x-125 is (3x-5)^3

Popular >

factor 27x^3-135x^2+225x-125

factor

27 x^{3} - 135 x^{2} + 225 x - 125

(3 x - 5)^{3}

Solution steps

27 x^{3} - 135 x^{2} + 225 x - 125

Use the rational root theorem

a_{0} = 125, a_{n} = 27

The dividers of

a_{0} : 1, 5, 25, 125,

The dividers of

a_{n} : 1, 3, 9, 27

Therefore, check the following rational numbers:

\pm \frac{1 , 5 , 25 , 125}{1 , 3 , 9 , 27}

\frac{5}{3}

is a root of the expression, so factor out

3 x - 5

= (3 x - 5) \frac{27 x ^{3} - 135 x ^{2} + 225 x - 125}{3 x - 5}

\frac{27 x ^{3} - 135 x ^{2} + 225 x - 125}{3 x - 5} = 9 x^{2} - 30 x + 25

= 9 x^{2} - 30 x + 25

Factor

9 x^{2} - 30 x + 25 : (3 x - 5) (3 x - 5)

= (3 x - 5) (3 x - 5) (3 x - 5)

Refine

= (3 x - 5)^{3}

x^{3} + 6 x^{2} + 12 x + 16

(a^{- 1})^{- 1}

\frac{( ( x - 3 ) ( x + 1 ) + 7 )}{( x - 4 )}

a^{12} - b^{12}

(11 a^{16} b^{3}) (\frac{4 a ^{3} b ^{6}}{c ^{8}})^{- 5}

What is factor 27x^3-135x^2+225x-125 ?
The solution to factor 27x^3-135x^2+225x-125 is (3x-5)^3