# How do you divide (5x^3 - 7x^2 + 14) / (x^2 - 2)?

Dec 18, 2015

Solution: $\left(5 x + 3\right) + \frac{6 x + 14}{x + 2}$ or

$\left(5 x + 3\right) + \frac{2 \left(3 x + 7\right)}{x + 2}$

#### Explanation:

Polynomial long division like so

Step 1 : Write the numerator in descending order, place wherever there is a missing variable, like $0 x$

Step 2 : Start diving. Ask yourself how many time is $\frac{5 {x}^{3}}{x} ^ 2$

Step 3: Multiply the quotient from step 2, to the divisor and subtract form dividend.

Repeat step 2 and 3 until we can't divide any more.

The quotient for polynomial division is $Q \left(x\right) + \frac{R \left(x\right)}{d \left(x\right)}$

Q(x) = Quotient
R(x) = Remainder
d= divisor

{: (,,5x,+3,,), (,,"-----","-----","-----","-----"), (x^2-2,")",5x^3,-7x^2,+0x,+14), (,,5x^3,-10x^2,,), (,,"----","-----",,), (,,,3x^2,+0x,), (,,,3x^2,-6x,), (,,,"-----","----",), (,,,,6x,+14) :}