Question

If one of the zeros of the polynomial p(x) is 2 then which of the following is a factor of p(x)?

• A. x - 2
• B. x + 2
• C. x - 1
• D. x + 1

Hint:

The relationship is simple: if the zero is a positive number `a`, the factor is `(x - a)`. If the zero is a negative number `-a`, the factor is `(x - (-a))` which is `(x + a)`.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question is based on the Factor Theorem. The Factor Theorem states that if \(x = a\) is a zero (or root) of a polynomial \(p(x)\), then \((x - a)\) is a factor of that polynomial.

Step 2: Key Formula or Approach:
According to the Factor Theorem, if \(a\) is a zero, then \((x-a)\) is a factor.

Step 3: Detailed Explanation:
We are given that one of the zeros of the polynomial \(p(x)\) is 2.
This means that when we set \(x = 2\), \(p(2) = 0\).
Using the Factor Theorem with \(a = 2\), the corresponding factor is \((x - a)\), which is \((x - 2)\).

Step 4: Final Answer:
The factor of \(p(x)\) is x - 2.