What is ((2x^4+4x^3+2x^2+8x+8))/((x+2)) ?

The solution to ((2x^4+4x^3+2x^2+8x+8))/((x+2)) is 2(x+1)(x^2-x+2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((2x^4+4x^3+2x^2+8x+8))/((x+2))

simplify

\frac{( 2 x ^{4} + 4 x ^{3} + 2 x ^{2} + 8 x + 8 )}{( x + 2 )}

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

Solution steps

\frac{2 x ^{4} + 4 x ^{3} + 2 x ^{2} + 8 x + 8}{x + 2}

Factor

2 x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 8 : 2 (x^{4} + 2 x^{3} + x^{2} + 4 x + 4)

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

Use the rational root theorem

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

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

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

Factor

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

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

Cancel the common factor:

x + 2

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

(38 x + 61 y) - (3 x - 11 y)

(6 - 2 x - x^{2})^{2}

- y^{2}

\frac{csc ( x )}{sin ( x )}

2 b^{- 7}

What is ((2x^4+4x^3+2x^2+8x+8))/((x+2)) ?
The solution to ((2x^4+4x^3+2x^2+8x+8))/((x+2)) is 2(x+1)(x^2-x+2)