1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
1/4 of all telephones at the office have built-in speaker phones 1/2 of the phone with the built in speaker phones have conferen
neonofarm [45]

Answer:

1/8

Step-by-step explanation:

1/2 of 1/4 is 1/8

7 0
3 years ago
50% of 30, hurry &lt;3<br> its saying my question is too short so ignore what im saying rn
9966 [12]

Answer:

The answer is 15

Step-by-step explanation:

50% of 30

30 × 50 ÷ 100 = 1500/100 = 15

Thus, The answer is 15

<u>-TheUnknownScientist</u><u> 72</u>

3 0
2 years ago
Read 2 more answers
AHHHH please help answer and I’ll give you points
german

Answer: Yes She is correct

Step-by-step explanation:

4 0
3 years ago
5. Vena finds lost balls and sells them. After selling 13, she had 22 balls left. How many golf balls did Vena have
Olenka [21]

Answer:35

Step-by-step explanation:

22+13=35

5 0
3 years ago
Farmer Brown planted corn and wheat on his 430 acres of land. The cost of planting and harvesting corn (which includes seed, pla
a_sh-v [17]

Answer:

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • A recipe used 1/4 cup of sugar for every 2 teaspoons of cocoa.
    14·1 answer
  • Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your way home, you travel at an average r
    13·1 answer
  • The product of two positive rational numbers is greater than either factor.is sometimes true
    10·1 answer
  • Jeremiah is making monthly payments of $66.00 to pay off a loan that he took out to buy a drum set, But he wants to pay off his
    7·2 answers
  • Find an equation of the line parallel to the line y=5 and passing through -2,-3
    10·1 answer
  • Find the values of k so that each remainder is three. <br> 10. (x^2+ 5x + 7) = (x + k)
    7·1 answer
  • Is the equation y=4x+1 proportional? *<br> Yes<br> No
    10·1 answer
  • These are isosceles equatorial triangle questions
    12·1 answer
  • SOMEONE HELP<br> Find sinD, sinE, cosD, and cosE. Write each answer as a fraction in simplest form.
    5·1 answer
  • PLZ HELP MEEEEEEEEEEE​
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!