[tex]We \ first, \ simplify \ \frac{125}{2} \\ \\ \left[\begin{array}{ccc}((x^3)-( \frac{125}{2}*x))-10 \end{array}\right] \\ \\ \boxed{\boxed{x^3= \frac{x^3}{1} = \frac{x^3*2}{2} }} \\ \\ \\ \boxed{ \frac{x^3*2-(125x)}{2} = \frac{2x^3-125x}{2} } \\ \\ \\ \frac{(2^3-125x}{2} -10 \\ \\ pulling \ out \ like \ factors : \\ \\ 2x^3 - 125x = x * (2x^2 - 125) \\ \\ Factoring: \ 2x^2 - 125 [/tex]
Here's how!
[tex]Proof : \ (A+B) * (A-B) =\\
A2 - AB + BA - B2 =\\
A2 - AB + AB - B2 = \\
A2 - B2\\[/tex]
Therefore . . .
[tex]\boxed{ \frac{x*(2x^2-125)-(10*2)}{2} = \frac{2x^3-125x-20}{2} } [/tex]
The factors would then be the following:
→ [tex]( Leading \ Coefficient : 1,2)[/tex]
→ [tex](Trailing Constant) : 1 ,2 ,4 ,5 ,10 ,20 [/tex]
By then, understanding on how we have got in our terms, such as the like terms, and also how we have understanded the coefficient's, we would then have our answer clear below.
[tex]\leadsto \ Your \ answer: \boxed{\bf{ \frac{2x^3-125x-20}{2} }}[/tex] ✔
