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
ahrayia [7]
3 years ago
15

Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros -4,-2,5. write the functio

n in standard form.
Mathematics
1 answer:
OLga [1]3 years ago
3 0

Answer:

Step-by-step explanation:

This is a third degree polynomial since we have 3 zeros.  We find these zeros by factoring the given polynomial.  The zeros of a polynomial are where the graph of the function goes through the x-axis (where y = 0).  If x = -4, the factor that gives us this value is (x + 4) = 0 and solving that for x, we get x = -4.  If x = -2, the factor that gives us that value is (x + 2) = 0 and solving that for x, we get x = -2.  Same for the 5.  The way we find the polynomial that gave us these zeros is to go backwards from the factors and FOIL them out.  That means that we need to find the product of

(x + 4)(x + 2)(x - 5).  Do the first 2 terms, then multiply in the third.

(x+4)(x+2)=x^2+2x+4x+8, which simplifies to

x^2+6x+8

No we multiply in the final factor of (x - 5):

(x^2+6x+8)(x-5)=x^3+6x^2+8x-5x^2-30x-40 which simplifies to

f(x)=x^3+x^2-22x-40

If you are aware of the method for factoring higher degree polymomials, which is to use the Rational Root Theorem and synthetic division, you will see that this factors to x = -4, -2, 5.  If you know how to use your calculator, you will find the same zeros in your solving polynomials function in your apps.

You might be interested in
HELP PLEASE!! TON OF POINTS. RIGHT ANSWERS ONLY REWARDED. MATH GENIUSES?
Nonamiya [84]

Answer:

The graph is shifted 1 unit right

The graph is shifted 2 units down

Step-by-step explanation:

We are given

Parent function as

f(x)=2^{x+3}-3

New function as

g(x)=2^{x+2}-1

we can also write as

g(x)=2^{x+3-1}-3+2

We can see that

1 is subtracted to x-value

and 2 is added to y-value

So, f(x) is shifted right by 1 unit

and

f(x) is shifted up by 2 unit


3 0
3 years ago
Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
tamaranim1 [39]

The answer is the third one: 32 inches

3 0
3 years ago
The function Q(x)=2x^2-kx+18. For what value of k does Q(x) have one distinct real solution? (NEEDS TO BE DONE WITHIN 2 HOURS!)
Aliun [14]

Answer:

k = 12

Step-by-step explanation:

Given:

The equation Q(x)=2x^2-kx+18

To find:

Value of k = ? for which the given equation has one distinct real solution.

Solution:

The given equation is a quadratic equation.

There are always two solutions of a quadratic equation.

For the equation: ax^{2} +bx+c=0 to have one distinct solution:

b^2 - 4ac = 0

Here,

a = 2,

b = -k and

c = 18

Putting the values, we get:

(-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12

The equation becomes:

Q(x)=2x^2-12x+18

And the one root is:

2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3

4 0
3 years ago
What is the sum of the measures, in degrees, of the interior angles of a 25-sided polygon?
inna [77]
Exterior angle = 360/25 =  14.4 degrees

internal angle = 180-14.4 = 165.6 degrees

sum of all the angles = 165.6*25 = 4140 degrees answer
4 0
3 years ago
As x increases without bound, f(x):
yarga [219]

Answer: Choice D) approaches y = -4

"x increases without bound" is another way of saying "x heads off to positive infinity". Visually, you follow the graph curve going to the right. As the graph shows, the curve steadily gets closer to the horizontal line y = -4, but it never actually gets there. This line is the horizontal asymptote.

7 0
3 years ago
Other questions:
  • Can all help me please
    9·1 answer
  • a ladder of length 4m leans against the wall of a house. The foot of the ladder is 2m from the wall. Will the ladder reach a win
    8·1 answer
  • Prove that the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle.
    8·1 answer
  • Solve for x.<br> X/8 = 4 <br> X=?<br><br> Anyone know??
    15·2 answers
  • What temperature is 23 above freezing in fahrenheit
    9·2 answers
  • Select the decimal that is equivalent to the fraction 57 over 100
    8·1 answer
  • You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to h
    12·2 answers
  • A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it has grown 9 inches,
    10·1 answer
  • It takes Serina 0.25 hours to drive to school. Her route is 16 km long. What is Serina’s average speed on her drive to school?
    11·1 answer
  • Let f(x) = 5x + 2 and g(x) = x² + 2x + 5. Evaluate the following.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!