Write the quadratic equation whose roots are −6 and 4, and whose leading coefficient is 4. (Use the letter x to represent the variable.)

4(x-4)(x+6)

Standard form: 4x^2+8x-96

Step-by-step explanation:

Since the roots are set to be -6 and 4, we need to find 2 linear equations that are equal to 0 when x is at -6 and when x is at 4, and multiply them together. That would look like this:

(x-4)(x+6)

Notice how if I plug in 4 or -6 for x, the whole thing is going to be 0.

Now, if we were to factor this, the leading coefficient would be 1. Since we want to change the leading coefficient while still preserving our roots, we can just multiply the whole polynomial by 4:

4(x-4)(x+6)

Notice if I still plug in 4 or -6 for x, the whole thing is going to be 0.

In standard form, the polynomial would be 4x^2+8x-96.