Question

Which statements are true about the polynomial function?

Answer 1

F(-2)  = -8 + 20 - 12 = 0  so first choice is correct

x^3 + 5x^2 + 6x = x(x^2 + 5x + 6) = x(x + 3)(x + 2)

so second choice is incorrect and third choice is correct

when x = 2  f(x) = 8 + 20 + 12 = 40 so last choice is incorrect.

Answer 2

Answer:

f(−2)=0

(x+2) is a factor of f(x) .

Step-by-step explanation:

f(x)=x^3+5x^2+6x

LEts factor f(x)

f(x)= x(x^2 +5x+6)

product is 6 and sum is 5

3*2= 6  and 3+2=5

f(x)= x(x+2)(x+3)

Now we check with each option

f(-2)= 0

LEts plug in -2 for x in f(x)

f(x)=x^3+5x^2+6x

f(-2)= (-2)^3 + 5(-2)^2 + 6(-2)= -8 +20-12= 0

f(x) divided by (x−2) has a remainder of 0

f(x)= x(x+2)(x+3)

f(x) does not have factor x-2 so f(x) is not divisible by (x-2)

(x+2) is a factor of f(x)

f(x)= x(x+2)(x+3)

f(x) have factor x+2 so (x+2) is a factor of f(x)

when x=2, f(x)=0

LEts plug in 2 for x in f(x)

f(x)=x^3+5x^2+6x

f(-2)= (2)^3 + 5(2)^2 + 6(2)= 8 +20+12= 40