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
saveliy_v [14]
3 years ago
12

I am confused in this can someone help?

Mathematics
1 answer:
fgiga [73]3 years ago
8 0

Answer:

\huge\boxed{\sf a = -12 , b = 8}

Step-by-step explanation:

<u>Given polynomial is:</u>

f(x) = ax^3+ b^2 + 3x + 4

\rule[225]{225}{2}

First factor is (x-1)

Let x - 1 = 0  => x = 1

Putting this in the above polynomial

f(1) = a(1)^3 + b(1)^2 + 3(1) + 4

Given that it's remainder is 3

3 = a + b + 3 + 4

3 = a + b + 7

Subtracting 7 to both sides

-4 = a + b\\OR \\

<h2>a + b = -4 -------------------------- (1)</h2>

\rule[225]{225}{2}

Second Factor is 2x + 1

Let 2x + 1 = 0 => x = - 1 / 2

Putting in the above polynomial

f(-\frac{1}{2} ) = a (-\frac{1}{2} )^3 + b (-\frac{1}{2} )^2  + 3 (-\frac{1}{2} ) + 4

The remainder is 6

6 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2} + 4\\6 - 4 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2}\\2 = \frac{-a + 2b -12 }{8} \\-a + 2b - 12 = 16\\-a + 2b = 16 + 12\\

<h2>-a + 2b = 28  --------------------------------(2)</h2>

\rule[225]{225}{2}

Adding both equations

a + b -  a + 2b = -4 + 28

3b = 24

Dividing both sides by 3

b = 8

\rule[225]{225}{2}

Putting b = 8 in Equation (1)

a + 8 = -4

a = - 4 - 8

a = -12

\rule[225]{225}{2}

You might be interested in
The perimeter of a rectangle is 50 cm and the length is 4 cm longer than the width. Write and solve the system of equations usin
k0ka [10]
P=2(l+w)
50=2(4+w)
50=8+2w
collect the like terms 50-8=2w
42=2w divide both sides by 2
w=21

6 0
3 years ago
The histogram shows the number of text messages sent by two high school juniors on one monday. Which statement most reasonably e
beks73 [17]

Answer:

The students where asleep and did not have phones turned on.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help me with this for brainliest
frez [133]

Answer: B. z-311+311=151+311

Step-by-step explanation:

You do the opposite since you want to get rid of 311

8 0
2 years ago
Read 2 more answers
5/3x+1/3x=26 2/3+7/3x<br>solve for X​
Marat540 [252]

Let's solve your equation step-by-step.

5 /3 x+  1 /3 x=  262 /3  + 7 /3  x

x=−262

Description:

The first step is to simplify the equation step by step and to simplify an equation you can first multiplying the factors and use the exponent rules to remove the parentheses. After that youneed to combine it a terms. Then you will get your answer.

Answer:  x=−262

Hope this helps.

7 0
3 years ago
Betty has an order for 160 hair bows. She can make 16 hair bows per day. Which is a reasonable answer?
marta [7]

Answer:

10 days

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, if she makes 16 bows per day, it would take her 10 days because 160/16=10

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

7 0
3 years ago
Read 2 more answers
Other questions:
  • The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.
    9·2 answers
  • Trigonometry
    11·2 answers
  • Will give 20 pts! pls answer
    15·2 answers
  • You have been cleaning this diesel dispenser for 35 minutes you have completed 6 dispensers how many minutes has it taken you to
    12·2 answers
  • The slope of the line below is -8/7.
    11·1 answer
  • Its about number lines, thanks <br> no links<br> SORRY IF THE LIGHTING IS BAD
    6·2 answers
  • A house that was originally listed for sale at $450,000 has decreased the asking price by 8%. By how much has the price been red
    9·1 answer
  • Which expression is equivalent to a^-x<br> A. a^1/x<br> B. -a^x<br> C. 1/a^x <br> D. -1/a^x
    9·1 answer
  • Determine if each statement is true or false
    12·1 answer
  • Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5),
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!