# How do you long divide (2x^3+5x^2-36x+27) ÷ ( x-2)?

Dec 20, 2015

Answer: $\left(2 {x}^{2} + 9 x - 18\right) - \frac{9}{x - 2}$

#### Explanation:

Polynomial long division like so

Step 1 : Write the numerator in descending order

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

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

{: (,,color(white)("XX")2x^2,color(white)("XX")+9x,color(white)("XX")-18,), (x-2,")",bar(color(white)("XX")2x^3),bar(color(white)("XX")+5x^2),bar(color(white)("XX")-36x),bar(color(white)("XX")+27)), (,,color(white)("XX")2x^3,color(white)("XX")-4x^2,,), (,,bar(color(white)("XXX")),bar(color(white)("XX")9x^2),bar(color(white)("XX")-36x),bar(color(white)("XX")+27)), (,,,color(white)("XX")9x^2,color(white)("XX")-18x,), (,,,bar(color(white)("XXX")),bar(color(white)("XX")-18x),bar(color(white)("XX")+27)), (,,,,color(white)("XX")-18x,color(white)("XX")+36), (,,,,bar(color(white)("XXXX")),bar(color(white)("XXXX")-9)) :}