Final answer:
To find the remainder of the polynomial 2x^2 + 7x - 39 divided by x - 7, we apply the Remainder Theorem by substituting x with 7 in the polynomial, which gives us 2(7)^2 + 7(7) - 39. Upon simplifying, we get a remainder of 108.
Step-by-step explanation:
To find the remainder of 2x^2 + 7x - 39 divided by x - 7, we can use either polynomial long division or synthetic division. However, there's also a shorthand method using the Remainder Theorem which states that the remainder of a polynomial f(x) divided by x - k is simply f(k).
Applying the Remainder Theorem: we evaluate the polynomial at x = 7.
Replace x in the polynomial with 7: 2(7)^2 + 7(7) - 39.
Calculate the result: 2(49) + 49 - 39 which simplifies to 98 + 49 - 39 = 108.
So, the remainder is 108.
Note that the information provided involving quadratic equations and solving for x is not directly relevant to finding the remainder when dividing a polynomial by a linear factor.