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Let h(x) be a polynomial such that h(-1/...

Let h(x) be a polynomial such that `h(-1/3) =0`, then one of the factors of h(x) is

A

3x-1

B

3x+1

C

x-3

D

x+3

Text Solution

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The correct Answer is:
To find one of the factors of the polynomial \( h(x) \) given that \( h\left(-\frac{1}{3}\right) = 0 \), we can use the Factor Theorem. Here are the steps to solve the problem: ### Step-by-Step Solution: 1. **Understanding the Factor Theorem**: The Factor Theorem states that if \( h(a) = 0 \) for some value \( a \), then \( (x - a) \) is a factor of the polynomial \( h(x) \). 2. **Identifying the Value of \( a \)**: In this case, we are given that \( h\left(-\frac{1}{3}\right) = 0 \). Thus, we can identify \( a = -\frac{1}{3} \). 3. **Formulating the Factor**: According to the Factor Theorem, since \( h\left(-\frac{1}{3}\right) = 0 \), the corresponding factor will be: \[ x - a = x - \left(-\frac{1}{3}\right) = x + \frac{1}{3} \] 4. **Rewriting the Factor**: To express this factor in a more standard form, we can multiply through by 3 to eliminate the fraction: \[ 3\left(x + \frac{1}{3}\right) = 3x + 1 \] Thus, one of the factors of \( h(x) \) is \( 3x + 1 \). ### Final Answer: One of the factors of \( h(x) \) is \( 3x + 1 \). ---
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