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

Step 1: Understanding the Concept:
The zeroes of a polynomial are the values of \( x \) for which the value of the polynomial becomes zero. The number of zeroes corresponds to the degree of the polynomial.
Step 2: Detailed Explanation:
The given polynomial is \( p(x) = (x - 2)(x + 3) \).
If we multiply the factors, we get:
\[ p(x) = x^2 + 3x - 2x - 6 = x^2 + x - 6 \]
The degree of this polynomial is 2, which indicates it is a quadratic polynomial.
To find the zeroes, set \( p(x) = 0 \):
\( (x - 2)(x + 3) = 0 \)
This implies either \( x - 2 = 0 \) or \( x + 3 = 0 \).
So, \( x = 2 \) and \( x = -3 \) are the two distinct zeroes.
Step 3: Final Answer:
The polynomial has two zeroes.