What is ((2x^4+8x^3+7x^2+4x+3))/((x+3)) ?

The solution to ((2x^4+8x^3+7x^2+4x+3))/((x+3)) is (x+1)(2x^2+1)

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simplify ((2x^4+8x^3+7x^2+4x+3))/((x+3))

simplify

\frac{( 2 x ^{4} + 8 x ^{3} + 7 x ^{2} + 4 x + 3 )}{( x + 3 )}

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

Solution steps

\frac{2 x ^{4} + 8 x ^{3} + 7 x ^{2} + 4 x + 3}{x + 3}

Use the rational root theorem

= \frac{( x + 1 ) \frac{2 x ^{4} + 8 x ^{3} + 7 x ^{2} + 4 x + 3}{x + 1}}{x + 3}

\frac{2 x ^{4} + 8 x ^{3} + 7 x ^{2} + 4 x + 3}{x + 1} = 2 x^{3} + 6 x^{2} + x + 3

= \frac{( x + 1 ) ( 2 x ^{3} + 6 x ^{2} + x + 3 )}{x + 3}

Factor

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

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

Cancel the common factor:

x + 3

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

(2 m + 3 n - 5 p)^{3}

(x^{9})^{0}

2^{\frac{3}{5}} \cdot x \cdot 2^{\frac{2}{3}}

(d^{4})^{3}

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

What is ((2x^4+8x^3+7x^2+4x+3))/((x+3)) ?
The solution to ((2x^4+8x^3+7x^2+4x+3))/((x+3)) is (x+1)(2x^2+1)