Questions: Which of the following is a factor of 5x^2-17x+6?

Transcript text: Which of the following is a factor of $5 x^{2}-17 x+6$

Solution

Solution Steps

To determine which of the given options is a factor of the quadratic expression $5x^2 - 17x + 6$, we can use the factor theorem. The factor theorem states that if $x = r$ is a root of the polynomial, then $x - r$ is a factor of the polynomial. We can find the roots of the polynomial using the quadratic formula and then check if any of the given options match $x - r$.

Step 1: Identify the Quadratic Expression

We are given the quadratic expression $5x^2 - 17x + 6$. Our goal is to determine which of the given options is a factor of this expression.

Step 2: Find the Roots of the Quadratic Expression

To find the factors, we first need to find the roots of the quadratic expression. The roots are the solutions to the equation $5x^2 - 17x + 6 = 0$. Solving this equation, we find the roots to be $x = \frac{2}{5}$ and $x = 3$.

Step 3: Determine the Factors from the Roots

According to the factor theorem, if $x = r$ is a root of the polynomial, then $x - r$ is a factor. Therefore, the factors corresponding to the roots are:

For $x = \frac{2}{5}$, the factor is $x - \frac{2}{5}$.
For $x = 3$, the factor is $x - 3$.

Final Answer

$\boxed{x - 3}$

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