Question

Divide : x³ - 6x² + 12x - 8 by x - 2​

Answer 1

Answer:

#(x^3-6x^2+12x-8)/(x-2)=(x-2)^3/(x-2) = (x-2)^2 = x^2-4x+4#

Explanation:

Another way to solve this problem is to factor the dividend polynomial to see if there are any factors which are the divisor!

One clue to try this is that the first term in the dividend, #x^3#, is the cube of the first term in the divisor, #x# and the last term, #-8# is the cube of the last term of the divisor #(-2)^3#. It seems that perhaps, if we are lucky, our polynomial is the cube of the divisor:

#(x-2)^3 = color(red)((x^2-4x+4))(x-2)=x^3-6x^2+12x-8#

In fact it is - and we can use the intermediate result in red above to find the answer to our question:

#(x^3-6x^2+12x-8)/(x-2)=x^2-4x+4#