Factor completely.   `2x(x^3)+5x(x^2)-8x-20`



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Wilson2014's profile pic

Posted on (Answer #2)

Method: Simplify first. Then factor by grouping. 


`=> 2x^4+5x^3-8x-20`

Factor by grouping. It becomes:  


=> `(x^3 - 4)*(2x+5)`

This cannot be factored anymore.

Therefore the completely factored expression is 


mathsworkmusic's profile pic

Posted on (Answer #4)

When faced with factorizing an equation of higher order than two, we can look for integer roots by looking at integer factors of the zeroeth term (in this case -20).

Trying 1,-1,2,-2,4,-4,5,-5 it can be seen that there is a root between -2 and -3.

Using the method of bifurcation we try -2.5 next. This provides a root: (2x+5).

We can then use algebraic long division to factor out the equation:

                `x^3 -4`

`2x+5 )` `overline (2x^4 + 5x^3 - 8x - 20)`

           `-2x^4 + 5x^3`

                                     `-8x - 20`

                                  `- -8x -20`



So the equation factorizes (fully) to (2x+5)(x^3-4). There are two real roots (implying two additional complex roots as the equation is order 4).

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