Question

Find the value of $q$, if $\sqrt{36x^4+24x^3+16x^2+qx+1}$ is a perfect square.

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (D)

$1$

$÷$	$6x^2+2x-1$ <= Quotient
$6x^2$	$36x^4+24x^3+16x^2+qx+1$ $36x^4$
$12x^2+2x$	$24x^3+16x^2$ $24x^3+4x^2$
$12x^2+4x-1$	$12x^2+qx+1$ $-12x^2-4x-1$
Remainder $\Rightarrow 0$

Since the given polynomial is a perfect square, we must have $q=4$.