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

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

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factor 2(x+1)^3-3(x+1)^2+5

factor

2 (x + 1)^{3} - 3 (x + 1)^{2} + 5

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

Solution steps

2 (x + 1)^{3} - 3 (x + 1)^{2} + 5

Use the rational root theorem

a_{0} = 5, a_{n} = 2

The dividers of

a_{0} : 1, 5,

The dividers of

a_{n} : 1, 2

Therefore, check the following rational numbers:

\pm \frac{1 , 5}{1 , 2}

- \frac{1}{1}

is a root of the expression, so factor out

(x + 1) + 1

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

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

= 2 (x + 1)^{2} - 5 (x + 1) + 5

Refine

= (x + 2) (2 (x + 1)^{2} - 5 (x + 1) + 5)

Expand

2 (x + 1)^{2} - 5 (x + 1) + 5 : 2 x^{2} - x + 2

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

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

\frac{1 - 4 x ^{2}}{1 - 2 x}

7 x + 70 - 79

(\frac{1 - 41}{4}) + 6

(4 b + 4) + (- 5 y + 2 x)

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