Question

Show that 2x + 1 is a factor of


`{2x}^(3) - {x}^(2) + 3x + 2`


PLS HELP ​

Answer 1

Explanation:

First, simply

`2x + 1 = x + 0.5`

This is useful because using the remainder Theorem,

If x-a is a factor of a Polynomial, P(X)., then P(a)=0.

Here the factor is

`x + 0.5`

Which can be written as

`x - ( - 0.5)`

So our a is -0.5, when then plug that in the polynomial.

`2( - 0.5) {}^(3) - ( - 0.5) {}^(2) + 3( - 0.5) + 2`

`2( - 0.125) - (0.25) - 1.5 + 2`

`- 0.25 - 0.25 - 1.5 + 2`

`- 0.5 - 1.5 + 2`

`- 2 + 2 =`

`0`

Since that satires the remainder Theorem, 2x+1 is a factor of the polynomial.