Question

give possible expressions for the length and breadth of the rectangle whose area is given by x²-5x+6

Answer 1

Answer:

The answer is $x-2,x-3$

Step-by-step explanation:

Given expression is

    $=x^2-5x+6$

Split the middle term and factor both the terms

   $=x^2-3x-2x+6\\=(x^2-3x)+(-2x+6)\\=x(x-3)-2(x-3)$

Factor out the common terms

   $=(x-3)(x-2)$

And since be know that area of a triangle is $\text{length}\times \text{breadth}$

Therefore possible length is $(x-2)$ and breadth is $(x-3)$ or vice versa