Question

$Solve:4yz(z^2+6z-16)÷2y(z+8)$

• A. $z-2$
• B. $z(z-2)$
• C. $2z(z-2)$
• D. $z(z-4)$

Answer 1

The correct option is C

$2z(z-2)$

Given, the expression is
$\frac{4yz(z^2+6z-16)}{2y(z+8)}.$

First, we will factorise $(z^2+6z-16).$

Comparing the above expression with the identity $x^2+(a+b)x+ab$, we note that,$(a+b)=6andab=-16.$

Since,
$8+(-2)=6and\left(8\right)(-2)=-16$,
the expression, $z^2+6z-16$
$=z^2+8z-2z-16$
$=z(z+8)-2(z+8)$
$=(z-2)(z+8)$ . . . (i)

By substituting (i) in the given expression, we get
$=\frac{4yz(z-2)(z+8)}{2y(z+8)}$
$=\frac{4\times y\times z\times (z-2)\times (z+8)}{2\times y\times (z+8)}$
$=2z(z-2)$