answer.
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
dusya
2 months ago
4

A student divided f(x) = 3x^3 + 3x^2 + 5x - 4 by x + 2 and found the remainder was r = -6. Based on the remainder theorem, what

can be concluded about f (x)?
Mathematics
1 answer:
PIT_PIT [12.4K]2 months ago
7 0

Answer:

Adjust the equation by subtracting the right side from both sides:

x - (3*x^3 + 8*x^2 + 5*x - 7) = 0

Step-by-step solution: Step 1: Equation after Step 1: x - ((((3*(x^3)) + 23x^2) + 5x) - 7) = 0 Step 2: Equation after Step 2: x - (((3x^3 + 23x^2) + 5x) - 7) = 0 Step 3: Step 4: Factoring common terms:

4.1 Extract common factors:

-3x^3 - 8x^2 - 4x + 7 =

-1 • (3x^3 + 8x^2 + 4x - 7)

Confirming if it is a perfect cube:

4.2 The expression 3x^3 + 8x^2 + 4x - 7 is not a perfect cube

Attempting to factor by grouping:

4.3 Factoring: 3x^3 + 8x^2 + 4x - 7

Thoughtfully divide the expression into groups, each consisting of two terms:

Group 1: 3x^3 - 7

Group 2: 8x^2 + 4x

Separate out terms from each group:

Group 1: (3x^3 - 7) • (1)

Group 2: (4x) • (2x + 1)

Step-by-step explanation:

You might be interested in
How many subsets are there in (a,b,c,d,e,f,h,i)?​
Inessa [12570]
The set encompasses 256 subsets. Step-by-step explanation: The elements in the set [a,b,c,d,e,f,h,i] total to 8. The total number of subsets is obtained using the formula

, where n signifies count of elements.

7 0
17 days ago
Marcia has a balance of $1700 on her credit card, which she plans to pay off by making a payment of the same amount each month.
PIT_PIT [12445]

Remaining balance on Marcia's credit card = $1700

Marcia believed she could clear her debt by making consistent monthly payments.

Given the four provided payment options, we need to determine which one will help her pay off her balance the quickest.

A.→ 55 × Number of months = 1700

Number of months = \frac{1700}{55}=31 months (approximately)

B. → 45 × Number of months = 1700

Number of months = \frac{1700}{45}=38 months (approximately)

C.→ 75 × Number of months = 1700

Number of months = \frac{1700}{75}=23 months (approximately)

D.→ 90 × Number of months = 1700

Number of months = \frac{1700}{90}=19 months (approximately)

Choosing to pay $90 monthly would allow Marcia to settle her balance in the shortest time.

8 0
13 days ago
Read 2 more answers
Alan and Judith begin withdrawing money from their accounts at the same time.
Svet_ta [12734]

Response:

Step-by-step breakdown:

N

4 0
1 month ago
lisa has played in 6 soccer matches. Her brother josh has played in 18 soccer matches. lisa saay josh has played in 12 times as
PIT_PIT [12445]

Answer:

Josh has participated in 12 more matches, not 12 times the amount she has played.

Step-by-step explanation:

Lisa's usage of the term 'times' made her statement inaccurate.

5 0
1 month ago
When comparing prices for activities at a local recreation center, you notice that the center charges different prices on differ
Zina [12379]
The variation in pricing is not due to the type of activity since it remains the same. Instead, the cost fluctuates based on the day of the week.
5 0
29 days ago
Read 2 more answers
Other questions:
  • The current global human population is about 6.1 billion and is growing at an annual rate of 1.35 percent. If world population w
    8·1 answer
  • A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75.
    13·1 answer
  • The graph of the function f(x) = (x – 4)(x + 1) is shown below. On a coordinate plane, a parabola opens up. It goes through (neg
    9·2 answers
  • Suppose that the weights of airline passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation
    8·1 answer
  • A teacher wants to see if a new unit on taking square roots is helping students learn. She has five randomly selected students t
    5·2 answers
  • Camry is a popular car manufactured by Japanese Car manufacturer, Toyota. Being one of the best selling cars in USA, all of the
    12·1 answer
  • A music buff wants to estimate the percentage of students at a midwestern university who believe that elvis is still alive. how
    6·1 answer
  • Ariel left her home at 9 a.m., driving at 45 mph. At 11 a.m. her brother left the home and started after her at 60 mph. At what
    6·2 answers
  • • Jamie is constructing shipping containers for a sporting goods store. The containers are to be rectangular prisms.
    8·1 answer
  • The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of ch
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!