Question

check whether please is equal 3 square + a square - 28 + 12 is a multiple of 3 s -2

Answer 1

P(s) =
$3 {s}^{2} + {s}^{2} - 20s + 12$
we have to check whether p(s) is multiple of
g(s)=
$3s - 2$
If p(s) is a multiple of g(s) then upon dividing P(s) by g(s) the remainder would be zero.

Applying Remainder theorem

$3s - 2 = 0$
S = 2/3

then P(2/3) =
$3 \times \ \frac{ {2}^{2} }{ {3}^{2} } + \frac{ {2}^{2} }{ {3}^{2} } - 20 \times \frac{2}{3} + 12$
=
$\frac{4}{9}$

So , Remainder is
$\frac{4}{9}$
Not 0 so , p(s) is not multiple of g(s).