Question

what is the quotient (125 – 8x3) ÷ (25 + 10x + 4x2)? –2x + 5 2x – 5 –2x – 5 2x + 5

Answer 1

ANSWER

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = - 2x+5$

EXPLANATION

We have been given the quotient,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} }$
to simplify.

We need to rewrite the numerator as difference of two cubes.

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ {5}^{3} - ( {2x})^{3} }{ 25 + 10x + 4 {x}^{2} }$

We need to make use of the difference of cubes formula,

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

We now let,
$a = 5 \: and \: b = 2x$

Then the numerator becomes,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 5 (2x) + {(2x)}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

This simplifies to,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 10x + 4 {x}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

We cancel out common factors to obtain,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)}{ 1}$

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = 5 - 2x$

Answer 2

Answer:

The quotient is (5-2x)

Step-by-step explanation:

Given the expression  $\frac{125-8{x}^{3}}{25+10x+4{x}^{2}}$

We have to simplify the above expression to find the quotient.

$\frac{125-8{x}^{3}}{25+10x+4{x}^{2}}$

⇒ $\frac{5^3-{2x}^{3}}{25+10x+4{x}^{2}}$

By the identity

${a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})$

Here, a=5 and b=2x

gives  ${5}^{3}-{2x}^{3}=5^2+5(2x)+(2x)^2=25+10x+4x^2$

∴ expression becomes

$\frac{125-8{x}^{3}}{25+10x+4{x}^{2}}=\frac{(5-2x)(25+10x+4x^2)}{25+10x+4{x}^{2}}=(5-2x)$

Hence, the quotient becomes (5-2x)