Question

1) What is the remainder when 3x3 - 4x2 - 14x + 3 is divided by3x+5?A)A.43B)wiu0WI)D)IM

Answer 1

The given polynomail is

`3x^3-4x^2-14x+3`

To be divided by

`3x+5`

Since the question requires to find the remainder

Then following remainder theorem

Set 3x+5 to zero and solve for x

`\begin{gathered} 3x+5=0 \\ x=-(5)/(3) \end{gathered}`

Substitute x=-5/3 into the given polynomial to get the remainder

`\begin{gathered} 3(-(5)/(3))^3-4(-(5)/(3))^2-14(-(5)/(3))+3 \\ =3(-(125)/(27))-4((25)/(9))+14((5)/(3))+3 \\ =-(125)/(9)-(100)/(9)+(70)/(3)+3 \\ =(-125-100+210+27)/(9) \\ =(12)/(9) \\ =(4)/(3) \end{gathered}`

Therefore, the remainder is

`(4)/(3)`