Question

find the remainder when f(x)= 9x³ - 3x² + 14x - 3 is divided by g(x) =(3x-1).
or
factorise a square + b square - 2ab + 2 B C - 2 ca
please give this answer

Answer 1

remainder=2x+1

thanks

Answer 2

To find the remainder than we can use remainder theorem
from g(x) find the value of x and put this value in f(x)

$3 x- 1 = 0 \\ x = \frac{1}{3}$
$f( \frac{1}{3} ) = 9 {( \frac{1}{3} )}^{3} - 3 {( \frac{1}{3}) }^{2} + 14( \frac{1}{3} ) - 3 \\ \\ = \frac{9}{27} - \frac{3}{9} + \frac{14}{3} - 3 \\ \\ = \frac{1}{3} - \frac{1}{3} + \frac{14}{3} - 3 \\ \\ = \frac{14}{3} - 3 \\ \\ = \frac{14 - 9}{3} \\ \\ = \frac{5}{3}$
is the remainder.

2) to factorise

${a}^{2} + {b}^{2} - 2ab + 2bc - 2ac \\ \\ = ( {a - b)}^{2} + 2bc - 2ac \\ \\ =( {a - b)}^{2} - 2c(a - b) \\ \\ = (a - b)(a - b - 2c)$