Question

14. Show that 2x - 1 is factor of 6x^3- x^2 + 3x - 2.
$step \: by \: step$
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Answer 1

Step-by-step explanation:

2x-1=0

2x=1

x=1/2

put the value of x in given equation

6×1/8-1/4+3/2-2

3/4-1/4+3/2-2

lcm =4

-9+9/4

0/4

0

if answer is 0 then we can say that it is a factor of given equation.

Answer 2

SOLUTION

Factor is 2x-1

=) 2x-1=0

=) 2x= 1

=) x= 1/2

Putting the value of x in cubic equation

$= > 6 {x}^{3} - {x}^{2} + 3x - 2 \\ = > 6( \frac{1}{2} ) {}^{3} - ( \frac{1}{2} ) {}^{2} + 3( \frac{1}{2} ) - 2 \\ \\ = > 6 \times \frac{1}{8} - \frac{1}{4} + \frac{3}{2} -2 \\ \\ = > \frac{6}{8} - \frac{1}{4} + \frac{3}{2} - 2 \\ \\ = > \frac{6 - 2 + 12 - 16}{8} \\ \\ = > \frac{4 - 4}{8} \\ \\ = > \frac{0}{8} = 0$

hope it helps ☺️