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
mariarad [96]
3 years ago
12

Let p be a polynomial function defined by p(x) = 2x^3+5x^2-6x-9. Use the fact that p(-4)=-33, p(-3)=0, p(-2)=7, and p(-1)=0 to r

ewrite the expression for p(x) as the product of linear factors.

Mathematics
1 answer:
Vesnalui [34]3 years ago
5 0

Answer:

  p(x) = (2x -3)(x+3)(x +1)

Step-by-step explanation:

p(-3) = 0 tells you that (x+3) is a factor.

p(-1) = 0 tells you that (x+1) is a factor.

The remaining factor can be (ax +b), so the function is ...

  p(x) = (ax +b)(x +3)(x +1)

Matching leading coefficients, we have ...

  ax³ = 2x³   ⇒   a = 2

Matching constant terms, we have ...

  b(3)(1) = -9    ⇒   b = -3

So, our factorization is ...

  p(x) = (2x -3)(x +3)(x +1)

_____

<em>Check</em>

We can see if our factored form matches the other two data points given.

  p(-4) = (-11)(-1)(-3) = -33 . . . . tells us the vertical scaling is correct

  p(-2) = (-7)(1)(-1) = 7 . . . . . . . additional check passes

__

The graph shows the original function (red) and the factored function (blue dots). They are identical.

You might be interested in
At an airport , it costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of h
avanturin [10]
C(x) = 5x + 2

This is because at 1 hour it only cost 7 dollars, so it should only have 2 added to the end. 
5 0
3 years ago
Chance can wash the car in 2 hours, while Sandy can wash the same car in 4 hours. How many hours would it take for them to wash
VashaNatasha [74]
<span>1 hour and 1/3rd of an hour
</span>
so A is right 
4 0
3 years ago
What type of number is -2i?
Iteru [2.4K]

Answer:

It is an imaginary number.

Step-by-step explanation:

In this example, the real number is -2 is being multiplied by the imaginary unit, i, which i can be also expressed as (√-1).

7 0
2 years ago
Please help with 1 , and 2 I really don’t understand this!
elena-s [515]
1. B
2. A

hope this helped
6 0
2 years ago
Read 2 more answers
Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 69 feet long and 2 feet wide. The local har
Flura [38]
First we should figure out how many times 2 goes into 69,(because each tile is 2 feet long) and I am going to do that by dividing 69 by 2. I got 34.5, so we can just say 35 to make it easier. So we now know we need 35 tiles, but they come in boxes of 6, so we will need to divide 35 by 6. It didn't make a full number (it was 5.833) but we need a full number of tiles so we will round up.

Our final number of how many boxes of tiles is 6.
6 0
3 years ago
Read 2 more answers
Other questions:
  • Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 num
    10·1 answer
  • Sam has 2 2/3 cups of dry cat food that he will divide equally among 3 cats
    8·2 answers
  • The figure shows ∆ABC inscribed in circle D. If m ∠CBD = 25°, find m ∠BAC, in degrees.
    12·1 answer
  • Determine the truth value of each of these statements if thedomainofeachvariableconsistsofallrealnumbers.
    5·1 answer
  • Whats the surface area?
    12·1 answer
  • The scatter plot shows the number of days that several homes have been for sale co.pared to the number of times the house has be
    14·2 answers
  • PLEASE ANSWER THE BLANKS ASAP
    9·1 answer
  • El reloj de Nuestra Basílica de Chiquinquirá señala cada hora con igual número de campanadas. Para indicar las 6 a.M. Tocó 6 vec
    8·1 answer
  • This homework is due tomorrow
    5·1 answer
  • The perimeter of rectangle field is 160m than find the area of field if its breath is 20m
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!