What is (2x^3+6x^2+6x+2)/(x+1) ?

The solution to (2x^3+6x^2+6x+2)/(x+1) is 2(x+1)^2

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simplify (2x^3+6x^2+6x+2)/(x+1)

simplify

\frac{2 x ^{3} + 6 x ^{2} + 6 x + 2}{x + 1}

2 (x + 1)^{2}

Solution steps

\frac{2 x ^{3} + 6 x ^{2} + 6 x + 2}{x + 1}

Factor

2 x^{3} + 6 x^{2} + 6 x + 2 : 2 (x^{3} + 3 x^{2} + 3 x + 1)

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

Apply cube of sum rule:

x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} = (x + y)^{3}

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Cancel the common factor:

x + 1

= 2 (x + 1)^{2}

(2 x x)^{2}

- 6 \cdot (- 1)

x^{2} 2 x^{2} + x^{3} 98

\frac{5}{4} - \frac{5}{2}

35 \times 9

What is (2x^3+6x^2+6x+2)/(x+1) ?
The solution to (2x^3+6x^2+6x+2)/(x+1) is 2(x+1)^2