which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and…

which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?\no f(x)=3(x + 5)(x + 4)(x - 2)(x - 9)\no f(x)=3(x - 5)(x - 4)(x + 2)(x + 9)\no f(x)=(x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)\no f(x)=(x - 5)(x - 5)(x - 5)(x - 4)(x + 2)(x + 9)

which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?\no f(x)=3(x + 5)(x + 4)(x - 2)(x - 9)\no f(x)=3(x - 5)(x - 4)(x + 2)(x + 9)\no f(x)=(x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)\no f(x)=(x - 5)(x - 5)(x - 5)(x - 4)(x + 2)(x + 9)

Answer

Explanation:

Step1: Recall factor - root relationship

If (r) is a root of a polynomial, then ((x - r)) is a factor.

Step2: Determine factors based on roots

For root (r=-4), factor is ((x + 4)); for (r = 2), factor is ((x - 2)); for (r=9), factor is ((x - 9)); for (r=-5) with multiplicity 3, factors are ((x + 5)(x + 5)(x + 5)).

Step3: Form the polynomial

The polynomial with leading - coefficient 1 is (f(x)=(x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)).

Answer:

(f(x)=(x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)) (the third option)