Write a quadratic equation in factored form that has solutions of $$ x=2 $$ and $$ x=- $$ a) $$ (x-2)(3 x+5)=0 $$ b) $$ (x+2)(5 x-3)=0 $$ c) $$ (x+2)(3 x-5)=0 $$ d) $$ (x-2)(5 x+3)=0 $$

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To write a quadratic equation in factored form that has solutions of $$ x=2 $$ and $$ x=-2 $$, we can use the factored form of a quadratic equation, which is given by:

$$
(x - r_1)(x - r_2) = 0
$$

where $$ r_1 $$ and $$ r_2 $$ are the roots of the equation.

Given the roots $$ x=2 $$ and $$ x=-2 $$, we can substitute these values into the equation:

$$
(x - 2)(x + 2) = 0
$$

Now, let's expand this expression to see if it matches any of the provided options:

$$
(x - 2)(x + 2) = x^2 - 4
$$

Now, we will check each option to see if it can be factored to yield the same roots.

1. **Option a:** $$ (x-2)(3x+5) = 0 $$
   - Roots: $$ x=2 $$ and $$ x=-\frac{5}{3} $$ (not a match)

2. **Option b:** $$ (x+2)(5x-3) = 0 $$
   - Roots: $$ x=-2 $$ and $$ x=\frac{3}{5} $$ (not a match)

3. **Option c:** $$ (x+2)(3x-5) = 0 $$
   - Roots: $$ x=-2 $$ and $$ x=\frac{5}{3} $$ (not a match)

4. **Option d:** $$ (x-2)(5x+3) = 0 $$
   - Roots: $$ x=2 $$ and $$ x=-\frac{3}{5} $$ (not a match)

None of the provided options yield the correct roots of $$ x=2 $$ and $$ x=-2 $$. The correct factored form for the quadratic equation with the given roots is:

$$
(x - 2)(x + 2) = 0
$$

Thus, the answer is not among the options provided.
None of the provided options correctly represent a quadratic equation with solutions $$ x=2 $$ and $$ x=-2 $$. The correct factored form is $$ (x - 2)(x + 2) = 0 $$.

Write a quadratic equation in factored form that has solutions of \( x=2 \) and \( x=- \) a) \( (x-2)(3 x+5)=0 \) b) \( (x+2)(5 x-3)=0 \) c) \( (x+2)(3 x-5)=0 \) d) \( (x-2)(5 x+3)=0 \)

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