The width of a rectangle is x+1, and the area is x^3+2x^2+5x-6 cm. What is the length of the rectangle?

Question

Explain each step and check.

Answer 1

Use synthetic division;
....................... x² + x + 4
x + 1 ) x^3 + 2x² + 5x - 6
........... x^3 + x²
........... .......... x² + 5x
........... .......... x² + x
................ ............. 4x - 6
................ ............. 4x + 4
................ ................... -10

You have x² + x + 4, with a remainder of -10, so the length is
x² + x + 4 -10/(x+1)

Answer 2

-1| 1 2 5 -6

-1| 1 2 5 -6
......\/
......1

-1| 1 2 5 -6
......\/ -1
......1 1

-1| 1 2 5 -6
......\/ -1 -1
......1 1 4

-1| 1 2 5 -6
......\/ -1 -1 -4
......1 1 4 -10

x^2 + x + 4 - [10/(x+1)] = length