What is expand ((x^3+4x^2+x-6))/(x+3) ?

The solution to expand ((x^3+4x^2+x-6))/(x+3) is x^2+x-2

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expand ((x^3+4x^2+x-6))/(x+3)

expand

\frac{( x ^{3} + 4 x ^{2} + x - 6 )}{x + 3}

x^{2} + x - 2

Solution steps

\frac{x ^{3} + 4 x ^{2} + x - 6}{x + 3}

Factor

x^{3} + 4 x^{2} + x - 6 : (x - 1) (x + 2) (x + 3)

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

Cancel the common factor:

x + 3

= (x - 1) (x + 2)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = x, b = - 1, c = x, d = 2

= xx + x \cdot 2 + (- 1) x + (- 1) \cdot 2

Apply minus-plus rules

+ (- a) = - a

= xx + 2 x - 1 \cdot x - 1 \cdot 2

Simplify

xx + 2 x - 1 \cdot x - 1 \cdot 2 : x^{2} + x - 2

= x^{2} + x - 2

\frac{7 ( 3 - 3 z ) ^{2}}{2}

\frac{12 x + 51}{( x + 5 ) ( x + 2 )}

(x^{2} + 3) e^{5} x - cos (2 x) e^{6} x

\frac{9 x + 18 + x ^{2}}{x ^{2} ( x + 2 )}

\frac{s - 2}{( s ^{2} + 6 s + 13 ) ^{2}}

What is expand ((x^3+4x^2+x-6))/(x+3) ?
The solution to expand ((x^3+4x^2+x-6))/(x+3) is x^2+x-2