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
If SA=1/2lp+B, find p<br><br> What is the formula for finding p?
Svet_ta [12734]
<span>To isolate p, start by subtracting B from both sides: SA-B=1/2lp. Next, multiply both sides by 2 to eliminate the 1/2: 2SA=lp. Finally, divide both sides by l to derive p: (2SA)/l=p.</span>
8 0
2 months ago
The profit function P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x) = R(x) – C(x). Andre
Svet_ta [12734]

Answer: 8x - 1200

Step-by-step explanation: I solved the problem

3 0
1 month ago
Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks for $200.25, $359.45, $125, and $299.35. Then
Leona [12618]
1,459.75 - 200.25 - 359.45 - 125.00 - 299.35 = 475.70

475.70 + 375.00 = 850.70

After settling the bills and deposit, her account shows a balance of $850.70
8 0
1 month ago
Read 2 more answers
Four pounds of bananas cost $1.96. how much does it cost per pound?
tester [12383]
4 pounds cost $1.96
1.96 / 4 gives $0.49 per pound. 
4 0
26 days ago
Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use:
Zina [12379]

Examining Talia's steps to derive the line equation, we identify the erroneous step as detailed below:
Step 1:
Select a point on the line, such as (2,5)
Step 2:
<span>Select another point on the line, such as (1, 3)
Step 3:
</span><span>Measure units to find the slope. The line moves 1 unit to the right and 2 units upward, resulting in a slope of
(5-3)/(2-1) = 2/1 = 2
Step 4:
</span><span>Apply these values in the point-slope form
y - y1 = m(x - x1)
y - 3 = 2(x - 1)
y = 2x + 1
Hence, the conclusion is:
</span><span>Step 4 is erroneous due to incorrect application of (1, 3) in the point-slope format.</span>

4 0
2 months ago
Read 2 more answers
Other questions:
  • Which graph shows the solution to the system of linear inequalities? x – 4y &lt; 4 y &lt; x + 1 Image for option 1 Image for opt
    6·1 answer
  • The number of pages in the U.S. tax code exceeds the number of pages in the King James Bible by 18,528. The combined number of p
    8·2 answers
  • The recipe makes enough stew for 6 people, and the ingredients cost $9.75. How much would it cost to serve 24 people? Use the ra
    12·3 answers
  • A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting
    13·1 answer
  • Rate at which risk of down syndrome is changing is approximated by function r(x) = 0.004641x2 − 0.3012x + 4.9 (20 ≤ x ≤ 45) wher
    6·1 answer
  • On your birthday you receive an iPhone valued at $899. The value of the iPad decreases by 25% each year. What will its value be
    13·2 answers
  • The oblique rectangular prism below has a length of 6 cm, a width of 8 cm, and a height of 7 cm.What is the area of the base of
    6·2 answers
  • Regular Hexagon ABCDEF rotates 240' counterclockwise about its center to produce hexagon A'B'C'D'E'F'. Which points will A' and
    14·2 answers
  • Rina is 6x+3/8 feet tall and Ryan is 5x+1/8 feet tall. How much taller is Rina than Ryan
    9·1 answer
  • How are the values of the eights related in 880?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!