Question

if (3x-2) is a factor of 3x^3+x^2+px+12 . find value p​

Answer 1

Step-by-step explanation:

put x =2/3 in the equation then you will get the value of p

Answer 2

Given,

$\rm{p(x) = {3x}^{3} + {x}^{2} + px + 12}$

$\rm{g(x) = 3x - 2} \\ \underbrace{\overbrace{ \bf x = \frac{2}{3} }}$

Now,

$\rm{}p \bigg( \frac{2}{3} \bigg) = 0 \\ \\ \sf = > {3\bigg( \frac{2}{3} \bigg)}^{3} + {\bigg( \frac{2}{3} \bigg)}^{2} + p{\bigg( \frac{2}{3} \bigg) }+ 12 = 0 \\ \\ \sf = > 3\bigg( \frac{8}{27} \bigg) + \frac{4}{9} + \frac{2p}{3} + 12 = 0 \\ \\ = > \sf\frac{8}{9} + \frac{4}{9} + \frac{2p}{3} + 12 = 0 \\ \\ = > \sf \frac{8 + 4 + 6p + 108}{9} = 0 \\ \\ \sf= > 120 + 6p = 0 \\ \sf = > \: \: \: \: \: 6p = - 120 \\ \\ \sf = > \: \: \: \: \: \frac{6p}{6} = \frac{ - 120}{6} \\ \\ \sf = > \: \: \: \: \: \: p = - 20$

Thus,

• Required value of p is (-20)