Question

Which polynomial function has a leading coefficient of 2, root - 4 with multiplicity 3, and root 10 with multiplicity 1?

Answer 1

Answer:

second option

Step-by-step explanation:

Given x = a, x = b are roots of f(x) then the factors are

(x - a) and (x - b)

and f(x) is the product of the factors

f(x) = a(x - a)(x - b) ← where a is a multiplier

If the roots have multiplicity then the factor is repeated

x = a with multiplicity 2, then factors are (x - a) and (x - a)

Here a = 2

x = - 4 with multiplicity 3, thus factors (x + 4 ), (x + 4), (x + 4)

x = 10 with multiplicity 1 has factor (x - 10)

Thus the polynomial function is

f(x) = 2(x + 4)(x + 4)(x + 4)(x - 10)