How do you check whether 7 + 3x is a factor of 3x^3 + 7x?

Answer 1

If 7+3x is a factor, then 3x+7=0 is a solution ---> x = -7/3

3(-7/3)^3 + 7 (-7/3) =

3(-343)/27 + -49/3 =

-1029/27 + -441/27

=-1470/27 is not zero, but quite negative.

-490/9 in fact.

So no, it is not a solution.

Moreover,

x^2 - (7/3)x + 70/9

___________________

3x + 7 | 3x^3 + 7x

3x^3 + 7x^2

----------------------------

-7x^2 + 7x

-7x^2 - (49/3)x

-------------------------

70/3 x

70/3x + 490/9

the remainder is -490/9 <---- notice the remainder is the same as f(-7/3) by theorem