Question

The area of a rectangular field is ( x3 – 3x2 +3x-1) sq. units, find the length of this field if its breadth is (x-1) units.

Answer 1

Step-by-step explanation:

since breadth is (x-1), it means it is a factor of the main equation.

x³ - 3x² + 3x -1

subtracting 2 and adding 2

=x³ -x² -2x² +3x - 1 - 2 +2

= (x³ - x²) - (2x² - 2) +(3x-3)

= x²(x-1) -2 (x²-1) + 3(x-1)

= x²(x-1) -2(x-1)(x+1) +3(x-1)

taking (x-1) common

= (x-1)(x² -2(x+1) +3)

= (x-1)(x²-2x+1)

length of rectangular field = (x²-2x+1)

also, you can use below method, if you are comfortable:

x³ - 3x² + 3x - 1

(x-1)(x²-2x+1) --while you can calculate like x³-2x²+x-x²+2x-1

hence, length of rectangular field = (x²-2x+1)