Question

Evaluate: $\sqrt{x^4+10x^3+35x^2+50x+25}$ (Use division method).

• A. $x^2-5x+5$
• B. $x^2+5x+5$
• C. $|x^2+5x+5|$
• D. $|x^2-5x+5|$

Answer 1

The correct option is C $|x^2+5x+5|$

$÷$	$x^2+5x+5$ <= Quotient
$x^2$	$x^4+10x^3+35x^2+50x+25$ $x^4$
$2x^2+5x$	$10x^3+35x^2$ $10x^3+25x^2$
$4x^2+10x+5$	$10x^2+50x+25$ $10x^2+50x+25$
Remainder $\Rightarrow 0$

The square root of $x^4+10x^3+35x^2+50x+25$ is $|x^2+5x+5|$