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Mamont248 [21]
3 years ago
8

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

Mathematics
1 answer:
RSB [31]3 years ago
3 0

Answer:

f(x)=2x^{3}+24x^{2}+82x+60

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

f(x)=a(x+6)(x+5)(x+1)

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

60=a(0+6)(0+5)(0+1)

60=a(6)(5)(1)

60=30a

a=2

so

f(x)=2(x+6)(x+5)(x+1)

Applying the distributive property

Convert to expanded form                  

f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60

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