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

Concept Used:

Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0

Explanation:

To check for (3x + 7) be a factor of (3x³ + 7x)
We have to divide 3x³ + 7x by 7 + 3x

If remainder comes out be 0 then (7 + 3x) will be a factor of (3x³ + 7x)

By long division method,

As remainder is not zero so (7 + 3x) is not a factor of (3x³ + 7x)
By Remainder theorem:
put 7 + 3 x = 0
we get x = –7/3
Now for checking out the remainder put x = –7/3 in (3x³ + 7x)
we get,
f(–7/3) = 3(–7/3)³ + 7 (–7/3)
f(–7/3) = – (343/9) – (49/3)
f(–7/3) = –490/9
which is not equal to zero and hence (7 + 3x) is not a factor of (3x³ + 7x).