What is factor x^3-6^2+11x+6 ?

The solution to factor x^3-6^2+11x+6 is (x-2)(x^2+2x+15)

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factor x^3-6^2+11x+6

factor

x^{3} - 6^{2} + 11 x + 6

(x - 2) (x^{2} + 2 x + 15)

Solution steps

x^{3} - 6^{2} + 11 x + 6

6^{2} = 36

= x^{3} - 36 + 11 x + 6

Group like terms

= x^{3} + 11 x - 36 + 6

Add/Subtract the numbers:

- 36 + 6 = - 30

= x^{3} + 11 x - 30

Use the rational root theorem

a_{0} = 30, a_{n} = 1

The dividers of

a_{0} : 1, 2, 3, 5, 6, 10, 15, 30,

The dividers of

a_{n} : 1

Therefore, check the following rational numbers:

\pm \frac{1 , 2 , 3 , 5 , 6 , 10 , 15 , 30}{1}

\frac{2}{1}

is a root of the expression, so factor out

x - 2

= (x - 2) \frac{x ^{3} + 11 x - 30}{x - 2}

\frac{x ^{3} + 11 x - 30}{x - 2} = x^{2} + 2 x + 15

= (x - 2) (x^{2} + 2 x + 15)

\frac{4 x + 16}{4 x ^{2} - 16}

\frac{4 x + 12 x - 6}{x y}

- \frac{x ^{2} - 2 x - 3}{x + 1}

(23 - 2)^{\frac{1}{2}}

(+ 6 m) - (+ 2)

What is factor x^3-6^2+11x+6 ?
The solution to factor x^3-6^2+11x+6 is (x-2)(x^2+2x+15)