Question

Check whether 7 + 3x is a factor of 3x³ + 7x.

Answer 1

7 + 3x will be a factor of 3x³ + 7x only if 7 + 3x divides 3x³ + 7x leaving no remainder.

Let p(x) = 3x³ + 7x

7 + 3x = 0

⇒ 3x = -7

`⇒ x = -7/3`

`therefore"Remainder "= 3(-7/3)^3+7(-7/3)`

                        `= -343/9-49/3`

                        `= -490/9`

                        `≠ 0`

∴ 7 + 3x is not a factor of 3x³ + 7x.

Answer 2

Let us divide (3x³ + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3x will be a factor of 3x³ + 7x.

By long division,

As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x³ + 7x.