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

Solution:

If we divide 3x3 + 7x by 7 + 3x and remainder comes out to be 0 then 7 + 3x will be a factor of 3x3 + 7x. The same can be checked by long division method or by factor theorem.

Using factor theorem,

p(x) = 3x3 + 7x

g(x) = 7 + 3x

Put g(x) = 0, i.e., 7 + 3x = 0

x = - 73

p-73 = 3-733 + 7-73

= -3439 - 493 = -343-1479

= -4909 ≠ 0

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