Which expression is a possible leading term for the polynomial function graphed below?

The expression is ⇒ x^4 - 45x² + 40x + 84

Step-by-step explanation:

From the graph:

∵ The zeroes of the functions are -7 , -1 , 2 , 6

∴ The factors of functions are (x + 7) , (x + 1) , (x - 2) , (x - 6)

∵ (x + 7)(x + 1) = x² + x + 7x + 7 = x² + 8x + 7

∵ (x - 2)(x - 6) = x² - 6x - 2x + 12 = x² - 8x + 12

∵ (x² + 8x + 7)(x² - 8x + 12) =

   x^4 - 8x³ + 12x² + 8x³ - 64x² + 96x + 7x² - 56x + 84 =

   x^4 - 45x² + 40x + 84

∴ f(x) = x^4 - 45x² + 40x + 84