Question

Your classmate asserted that x2 - 4x - 12 and 12 - 4x - x' has the
same factors. Is your classmate correct? Prove by showing your solution​

Answer 1

Given:

Two equations are :- $x^{2} -4x-12$  and $12 - 4x - x^{2}$ .

To Find:

Does both the equations have the same factor?

Solution:

firstly consider one equation,  $x^{2} -4x-12$

$x^{2} -4x-12 \\= x^{2} -6x+2x-12\\=x(x-6)+2(x-6)\\=(x-6)(x+2)$

therefore, $(x-6)(x+2)$ are the factor of  $x^{2} -4x-12$    ....(1)

Now, consider   $12-4x-x^{2}$

$12-4x-x^{2} \\=12-6x+2x-x^{2} \\=6(2-x)+x(2-x)\\=(2-x)(6+x)$

therefore, $(2-x)(6+x)$ are the factors of  $12-4x-x^{2}$     ....(2)

Thus , from equation (1) and (2) , we get

⇒ $x^{2} -4x-12$  and $12 - 4x - x^{2}$ does not have the same factor.

Result: my classmate assertion was wrong.