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
seraphim [82]
3 years ago
5

Please help me answer this question. Show steps and explain

Mathematics
1 answer:
salantis [7]3 years ago
3 0

Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:

... -6/1

Then the factors of p/q are the factors of 6, with either sign.

Factors of p/q: ±1, ±2, ±3.

There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)

Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...

... f(x) = (x +1)(x² +x -6)

You can continue to test the factors of p/q, or you can factor the quadratic to get ...

... f(x) = (x +1)(x -2)(x +3)

Another way to test the factors is to program your graphing calculator to evaluate the function f(x) for those factors. The result from my TI-84 is shown in the second attachment. That shows f(x) = 0 for x = -3, -1, and +2.

Test the factors: f({-3, -2, -1, 1, 2, 3}) = {0, 4, 0, -8, 0, 24}

This tells you the x-intercepts.

X-intercepts: -3, -1, 2

Of course, the y-intercept is just the constant in the function—the value of the function when x=0.

Y-intercept: -6

As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...

End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.

_____

A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)

You might be interested in
If f is a function such that f(b)-f(a)/b-a=2, then which of the following statements must be true?
solong [7]
Based on the type of equation, f(b) relates to y2, f(a) relates to y1, b relates to x2, and a relates to x1.  If we change those around we now get:
(y2 - y1)/(x2 - x1) which is the slope formula, or the average rate of change.  thus your answer would be C
3 0
3 years ago
What is 8x -5+2 x simplified
IgorC [24]

8x -5+2 x

8x+2x-5 ( combine like terms)

answer:

10x-5 or -5+10x

8 0
3 years ago
At a conference for 500 people, 30% of the participants are French, 15% are Americans, 5% are Germans, and are of other national
Olenka [21]
As said before, 160 is the correct answer
Please: Rate. Thank!
7 0
3 years ago
Read 2 more answers
(-6, 1) and 3, 5)<br> M= rise/run=(y2-y1)/(x2-x1)
Sergeeva-Olga [200]

Answer:

4/9

Step-by-step explanation:

The slope of these points would be: (5-1)/(3+6) = 4/9

7 0
3 years ago
No one was born ugly<br> we just live in a judgmental world
bogdanovich [222]

Answer:

Ikr >:(

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • 2/3 -4x + 7/2 = -9x + 5/6
    10·1 answer
  • Five times a number is greater then 25
    9·2 answers
  • What is the product of 8 and 54
    7·1 answer
  • Complete the equation of the graphed linear function. Write the slope in decimal form.
    6·2 answers
  • Maria makes beaded bracelets for sale . The materials for each bracelet cost $3.00 and she sells the bracelets for $8.25 each. T
    10·1 answer
  • Which name gives the most information about the shape below???
    12·2 answers
  • In each of the following examples, a consumer purchases just two goods: x and y. Based on the information in each of the followi
    12·1 answer
  • What's the equivalent expression after combining the like terms?<br> −3z−z
    10·1 answer
  • What is the missing number in the table?
    5·1 answer
  • Find the next two terms in the pattern 100,98,94,88,80…
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!