What is factor 12x^3-5x^2+1 ?

The solution to factor 12x^3-5x^2+1 is (3x+1)(4x^2-3x+1)

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factor 12x^3-5x^2+1

factor

12 x^{3} - 5 x^{2} + 1

(3 x + 1) (4 x^{2} - 3 x + 1)

Solution steps

12 x^{3} - 5 x^{2} + 1

Use the rational root theorem

a_{0} = 1, a_{n} = 12

The dividers of

a_{0} : 1,

The dividers of

a_{n} : 1, 2, 3, 4, 6, 12

Therefore, check the following rational numbers:

\pm \frac{1}{1 , 2 , 3 , 4 , 6 , 12}

- \frac{1}{3}

is a root of the expression, so factor out

3 x + 1

= (3 x + 1) \frac{12 x ^{3} - 5 x ^{2} + 1}{3 x + 1}

\frac{12 x ^{3} - 5 x ^{2} + 1}{3 x + 1} = 4 x^{2} - 3 x + 1

= (3 x + 1) (4 x^{2} - 3 x + 1)

5 y + 2 - 3 y

(x - y)^{3} - (x + y)^{3}

(3 x y - 2 y)^{3}

\frac{3}{( x ^{2} + 3 x )} - \frac{1}{x} - \frac{6}{( x ^{2} - 9 )}

50 a^{2} + 75 a^{2} \cdot b

What is factor 12x^3-5x^2+1 ?
The solution to factor 12x^3-5x^2+1 is (3x+1)(4x^2-3x+1)