Question

If a polynomial $p\left(x\right)$ can be written as $(ax-b)(ax+b)$ where:
(i) $1<a\le 3$
(ii) $2<b<4$
(iii) $a,b$ are integers.

Which of the following can be $p\left(x\right)$

• A. $4x^2-4$
• B. $4x^2-9$
• C. $9x^2-4$
• D. $9x^2-9$

Answer 1

Answer: (A), (C)

The correct options are
A $4x^2-4$
C $9x^2-4$

$\because$ $2<b<4$, the only possible value of b is 3 because b is an integer.

Also,
$1<a\le 3$

So, $a$ can be 2 or 3, because they are the only integers that satisfy this condition.

We know,
$(a+b)(a-b)=a^2-b^2$

$\therefore$
The polynomial can be ;
1) $(2x-2)(2x+2)=4x^2-4$
2) $(3x-2)(3x+2)=9x^2-4$