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
german
4 years ago
9

Factor the expression: -\lambda ^{3}+4\lambda ^{2}+4\lambda -16

Mathematics
1 answer:
Anit [1.1K]4 years ago
3 0

Answer:

-(\lambda -4)(\lambda -2)(\lambda +2)

Step-by-step explanation:

What we want to fator is:

-\lambda^3 + 4 \lambda^2 + 4\lambda - 16

There is no common factor, but let's factor it by grouping. The first two addends can be factor as follows:

-\lambda^3 + 4 \lambda^2 = \lambda^2(-\lambda + 4) = -\lambda^2(\lambda - 4)

the second addends can be factor as well:

4\lambda - 16 = 4(\lambda- 4).

Then our original expression can be rewritten like

-\lambda^3 + 4 \lambda^2 + 4\lambda -16=\lambda^2(\lambda - 4) + 4(\lambda - 4)

And here the (\lambda-4) is the common factor!

-\lambda^2(\lambda - 4) + 4(\lambda - 4) = (\lambda - 4)(-\lambda^2 + 4)

Finally, we can factor the quadratic expression as a difference of squares -\lambda^2 + 4 = 4 - \lambda^2 = (2+\lambda)(2-\lambda)

Ant we get

(\lambda - 4)(-\lambda^2 + 4)= (\lambda - 4)(\lambda + 2)(2-\lambda)

now, we can extract the negative sign from (2-\lambda), and we get

-(\lambda -4)(\lambda -2)(\lambda +2).

You might be interested in
Need help solving for X
Bond [772]
X= -2

look at the 6x-12 you divide -12 by 6 and get x=-2
6 0
3 years ago
Help me..........
beks73 [17]
Y+5x=-3 step-by-step
4 0
3 years ago
1. Your average daily balance on your charge card for the month of July is $855.28. If your card carries an annual interest rate
Nat2105 [25]
1. Using "exact" interest, your charge will be
.. I = Prt
.. I = $855.28*0.154*(31/365)
.. I = $11.19

2. It will take 52.01 months to pay off the loan.

3. Your payment on 15,250 for 4 years will be $363.41. The effective interest rate that payment represents on a loan of $15,000 is 7.604%

4. Todd's monthly payments will be $409.06, so his total outlay will be
.. tax+license + down payment + loan repayment
.. = 1200 +1000 +48*409.06
.. ≈ $21,835

4 0
3 years ago
¿Cómo influye el fenómeno de capilaridad en la vida de las plantas?
Arlecino [84]

Answer:

Plants use capillary action to bring water up the roots and stems to the rest of the plant. Therefore, if the plant could not do this the plant would die.

Step-by-step explanation:

3 0
3 years ago
The luxury tax threshold in a professional sports league is the amount in total payroll that teams must stay under to prevent be
VMariaS [17]

Answer:

A: The coefficient changes from 120 to 117, and the base changes from 1.033 to 1.035. The function that represents the second model is A(t)=117(1.035)^t.

Step-by-step explanation:

luxury tax you get only the amount that you need

6 0
3 years ago
Other questions:
  • Please answer this correctly without making mistakes
    15·2 answers
  • What is the simplified form of 4r + 5s – 16r + 3s?
    7·2 answers
  • You have a 4 x 6 photo of you and your friend. a. You order a 5 x 7 print of the photo. Is the new photo similar to the original
    13·1 answer
  • A person swims 11 miles downstream in the same time they can swim 7 miles up stream. The speed of the current is 4 miles per hou
    8·1 answer
  • How do you write<br> 25/4<br> as a percentage?
    7·2 answers
  • If you were given a fractional strip, that did not have any subdivisions marked like this one pictured below, how would you dete
    12·1 answer
  • Manuel se ha gastado 2/8 partes de la paga en ropa y 1/12 parte en dulces. ¿Qué fracción de la paga le queda?, ¿Si le dieron 45€
    9·1 answer
  • **!!URGENT!!** A line passes through the points (9,-2) and (-1,8). What is the y-intercept of this line?
    9·1 answer
  • Write a function in any form that would match the graph shown below
    15·1 answer
  • I need help ASAP, please save me.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!