Question

How many zeroes does p(x) = (x $-$ 2)(x + 3) have ?

• A. Zero
• B. One
• C. Two
• D. Three

Hint:

For a polynomial in factored form \( (x-a)(x-b)(x-c)... \), the number of factors gives the number of zeroes.

Answer 1

The Correct Option is C

To determine how many zeroes the polynomial p(x) = (x - 2)(x + 3) has, we need to understand the definition of a zero of a polynomial.

1. A zero of a polynomial is a value for x that makes the polynomial equal to zero.

2. Given the polynomial p(x) = (x - 2)(x + 3), we can find the zeros by setting each factor to zero:

   • Set x - 2 = 0. Solving this, we get x = 2.
   • Set x + 3 = 0. Solving this, we get x = -3.

3. The values x = 2 and x = -3 are the zeros of the polynomial. This means the polynomial has two distinct zeros.

4. Therefore, the number of zeros of the polynomial p(x) = (x - 2)(x + 3) is Two.

Thus, the correct answer is Two.