Question

Show that 2x + 1 is a factor of
${2x}^{3} - {x}^{2} + 3x + 2$


PLS HELP ​

Answer 1

Step-by-step 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.