Question

find the reminder when 3x cube- 6x square + 3x - 7/9 is divided by 3x-4​

Answer 1

We have,

$\huge f(x) = 3x - 4 \\ \\ \sf \rightarrow f(x) = 3x - 4 = 0 \\ \sf \rightarrow f(x) = \: \: \: \: \: \: \: \: \: \: x = \pink{\frac{4}{3} }$

And,

$\bf \large p(x) = {3x}^{3} - {6x}^{2} + 3x - \frac{7}{9}$

Now, Putting the value of x form the given f(x) in p(x)

$\bf \small p( \frac{4}{3}) = 3 {( \frac{4}{3} )}^{3} - 6 {( \frac{4}{3} )}^{2} + \cancel3( \frac{4}{ \cancel3} ) - \frac{7}{9} \\ \\ \sf \rightarrow \cancel3 \times \frac{64}{ \cancel{27} \: 9} - \cancel6 \times \frac{16}{ \cancel9} + 4 - \frac{7}{9} \\ \\ \sf \rightarrow \frac{64}{9} - \frac{32}{3} + 4 - \frac{7}{9} \\ \\ \sf \rightarrow \frac{64 - 96 + 36 - 7}{9} \\ \sf \rightarrow \frac{100 - 103}{9} = \frac{ \cancel{ - 3}}{ \cancel9} \\ \sf \rightarrow \red{- \frac{1}{3} }$

Hence, On dividing the given p(x) by provided f(x), then, the remainder would be $\bf \large{ \red{ - \frac{1}{3} }}$.

$<marquee>#BAL$