Determine whether the given value of x is a zero of the given polynomial or not: (2x + 3)(3x - 2); x = 2/3

Let p(x) = (2x + 3) (3x - 2)
If x = 2/3 is a zero of the polynomial p(x), then it must satisfy p(2/3) = 0.

So, on putting x = 2/3 in the above equation, we get:

p(2/3) = (2 × (2/3) + 3)(3 × (2/3) - 2)

= ((4/3) + 3)(2 - 2)

= ((4/3) + 3) × 0

= 0.
Therefore the given value of x is a zero of the given polynomial.