Question

show that the polynomial p(x) =3x³+x²-20x+12 is a mutiple of 3x-2​

Answer 1

Step-by-step explanation:

Given

p(x) =3x³+x²-20x+12

as we know that if 3x-2 is multiple then p(x) = 0

3x-2=0

x = 2/3

p(x) =3x³+x²-20x+12

p(2/3) =3(2/3)³+(2/3)²-20(2/3)+12

= 24/27+4/9-40/3+12

= ( 24+12-360+324 )/27

=(360-360)/27

= 0/27

= 0

hence p(x) = 0

so 3x-2 is a multiple of polynomial p(x) =3x³+x²-20x+12