Question

Calculate the quotient and the reminder by dividing f(x)=3x^3 - 5x^2 + x - 2 by g(x) = x + 2 .​

Answer 1

Answer:

Step-by-step explanation:

f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } + x - 2 g ( x ) = x + 2

Subtract 3x³ from each sides.

-5x^{2}+x-2gx=x+2-3x^{3}

Add 5x² to both sides.

x-2gx=x+2-3x^{3}+5x^{2}

Subtract x from both sides.

-2gx=x+2-3x^{3}+5x^{2}-x

Combine x and -x to get 0.

-2gx=2-3x^{3}+5x^{2}

The equation is in standard form.

\left(-2x\right)g=2+5x^{2}-3x^{3}

Divide both sides by -2x.

\frac{\left(-2x\right)g}{-2x}=\frac{2+5x^{2}-3x^{3}}{-2x}

Dividing bu -2x undoes the multiplication by -2x.

g=\frac{2+5x^{2}-3x^{3}}{-2x}

Divide 2-3x³ +5x² by -2x.

g=\frac{3x^{2}}{2}-\frac{5x}{2}-\frac{1}{x}