What is ((-21x^3-25x^2-3x+1))/((1+3x)) ?

The solution to ((-21x^3-25x^2-3x+1))/((1+3x)) is -(x+1)(7x-1)

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simplify ((-21x^3-25x^2-3x+1))/((1+3x))

simplify

\frac{( - 21 x ^{3} - 25 x ^{2} - 3 x + 1 )}{( 1 + 3 x )}

- (x + 1) (7 x - 1)

Solution steps

\frac{- 21 x ^{3} - 25 x ^{2} - 3 x + 1}{1 + 3 x}

Factor out

- 1 : - (21 x^{3} + 25 x^{2} + 3 x - 1)

= \frac{- ( 21 x ^{3} + 25 x ^{2} + 3 x - 1 )}{1 + 3 x}

Use the rational root theorem

= \frac{- ( x + 1 ) \frac{21 x ^{3} + 25 x ^{2} + 3 x - 1}{x + 1}}{1 + 3 x}

\frac{21 x ^{3} + 25 x ^{2} + 3 x - 1}{x + 1} = 21 x^{2} + 4 x - 1

= \frac{- ( x + 1 ) ( 21 x ^{2} + 4 x - 1 )}{1 + 3 x}

Factor

21 x^{2} + 4 x - 1 : (7 x - 1) (3 x + 1)

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

Apply the commutative law:

1 + 3 x = 3 x + 1

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

Cancel the common factor:

3 x + 1

= - (x + 1) (7 x - 1)

a + 2 a + 3 a

12 x^{2} - 22 x y + 8 y^{2}

[\frac{6 x - 3 x ^{2} - 4 x ^{3}}{2 x ^{3}}]

(\frac{6 - x}{3})^{3}

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

What is ((-21x^3-25x^2-3x+1))/((1+3x)) ?
The solution to ((-21x^3-25x^2-3x+1))/((1+3x)) is -(x+1)(7x-1)