Question

Factorize the following

$x^2-2x-99$

• A. $(x+9)(x-11)$
• B. $(x-9)(x-11)$
• C. $(x+9)(x+11)$
• D. None of these

Answer 1

Answer: (A)

$(x+9)(x-11)$

In the given polynomial $x^2-2x-99$,

The first term is $x^2$ and its coefficient is $1$.

The middle term is $-2x$ and its coefficient is $-2$.

The last term is a constant term $-99$.

Multiply the coefficient of the first term by the constant $1\times (-99)=-99$.

We now find the factor of $-99$ whose sum equals the coefficient of the middle term, which is $-2$ and then factorize the polynomial $x^2-2x-99$ as shown below:

$x^2-2x-99$

$=x^2-11x+9x-99$

$=x(x-11)+9(x-11)$

$=(x+9)(x-11)$

Hence, $x^2-2x-99=(x+9)(x-11)$.