Question

Check whether the polynomial :p(s) =3s^3+s^2-20s+12 is a multiple of 3s-2

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

p(s) = 3s³ + s² - 20s + 12

If 3s - 2 is multiple of p(s), then
s = 2/3

p(s) = 3(2/3)³ + (2/3)² - 20(2/3) + 12

0 = 3*8/27 + 4/9 - 40/3 + 12

0 = 8/9 + 4/9 - 120/9 + 108/9

0 = ( 8 + 4 - 120 + 108 )/9

0 = 120 - 120

0 = 0

Therefore 3s - 2 is multiple of given polynomial.

Hope it helps

Answer 2

hey!!!

p(s) = 3s³ + s² - 20s + 12

g(s) = 3s - 2
>> 3s - 2 = 0
= 3s = 2
= s = 2/3

on putting values :-

p(2/3) = 3(2/3)³ + (2/3)² - 20(2/3) + 12
= 3(8/27) + 4/9 - 40/3 + 12
= 8/9 + 4/9 - 40/3 + 12
= 12/9 - 40/3 + 12
= 4/3 - 40/3 + 12
= -36/3 + 12
= -12 + 12
= 0

remainder is 0, therefore 3s-2 is a factor of 3s³ + s² - 20s + 12

cheers!!!