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
BigorU [14]
2 years ago
11

Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x).

Mathematics
1 answer:
ioda2 years ago
8 0

Answer:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5)

Step-by-step explanation:

f(x) = 4x^3 + 11x2 - 104x + 105

has the coefficients {4, 11 -104, 105}.  We perform synthetic division using the given -7 as divisor:

-7   /   4      11     -104     105

                -28     119     -105

     -----------------------------------

          4      -17      15         0

Since the remainder is zero (0), we have shown that -7 is a zero of f(x).  The coefficients of the quotient (above) are {4, -17, 15}.  Let's try factoring the corresponding polynomial again using synthetic division.  Start out by using 5 as divisor and determining whether or not the remaindeer is zero:

5    /     4     -17      15

                    20     15

     -------------------------

             4        3     30           No, the remainder is 30 and so 5 is not a

                                               root of this quadratic.  Try the divisor 3 instead:

3     /     4      -17      15

                      12      -15

      ---------------------------

             4       -5        0        Yes, the remainder is 0 and so 3 is a root.

Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5).  Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.  

You might be interested in
If you roll two fair dice repeatedly, what is the probability that you will get a sum of 4 before you get a sum of 5 ? (a) (b) (
AlexFokin [52]

Answer:

The probability that you will get a sum of 4 before you get a sum of 5 is \frac{1}{12}

Step-by-step explanation:

Given : If you roll two fair dice repeatedly.

To find : What is the probability that you will get a sum of 4 before you get a sum of 5 ?

Solution :

When two dice are rolled the outcomes are

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Total number of outcomes = 36

Favorable outcome get a sum of 4 before you get a sum of 5 is (1,3) ,(2,2) and (3,1) = 3

The probability that you will get a sum of 4 before you get a sum of 5 is

P=\frac{3}{36}

P=\frac{1}{12}

Therefore, The probability that you will get a sum of 4 before you get a sum of 5 is \frac{1}{12}

5 0
3 years ago
Challenge You have 2 different savings accounts. For Account​ A, the simple interest earned after months is ​$. For Account​ B,
Debora [2.8K]

Answer and Step-by-step explanation:

The computation is shown below;

As we know that

The simple interest is

Simple interest = Principal × rate × time

For Account A, the principal would be

2 = Principal × 3.2% × 3

So, the principal is $20.83

For account B, the principal would be

38.50 = Principal × 2.2% × 30

So, the principal is $58.33

Now the interest for both the accounts are as follows

For account 1

= $20.83 × 3.2%

= $0.67

And, for the account 2

= $58.33 × 2.2%

= $1.28

As it can be seen that the account 2 has the highest interest

The same is to be considered

7 0
2 years ago
Pablo will take the 11:43 AM train to San Diego. The train is estimated to arrive in San Diego in 3 hours 45 minutes. What is th
11Alexandr11 [23.1K]

Answer:

3. 28pm

Step-by-step explanation:

11  43

+3 45

15 28

15.28-12

=3.28

5 0
2 years ago
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends a
Natasha_Volkova [10]

Answer:

16 friends

Step-by-step explanation:

Right at the beginning, you can take the 2 chocolates Jack was left with out of the 50 chocolates Jack had at the beginning. That equals 48 chocolate bars, so we know that Jack gave his friends a total if 48 chocolates

50 - 2 = 48

Now that you have the number 48, you are really close to the answer.

If you know that he gave each if his friends 3 chocolates, you can make that into an equation and put it into a calculator. That would look like this:

48 \div 3 = 16

The reason you do 48 ÷ 3 is because Jack divided his 48 chocolates into groups of 3 to give to each of the other kids.

You get the answer 16, which means the answer is 16 kids at his friend's birthday party.

3 0
3 years ago
Help Me With This Question Please!
Stolb23 [73]

i think the answer is 1265

7 0
3 years ago
Read 2 more answers
Other questions:
  • I’m horrible at graphing please help it says to graph a line with the slope 1/3 passing through the point (3,1)
    11·1 answer
  • Which is independent and which is dependent.
    14·1 answer
  • Andrew is buying pencils, and he wants to buy fewer than 25. He plans to give 75% of the pencils to his students and save three
    9·2 answers
  • The total bill of a meal at a restaurant is 25x – 115. Five friends agree to split the cost of the meal equally. What could you
    10·2 answers
  • $99 for 12 CDs unit rate
    9·2 answers
  • Describe one kind of diagram you might draw to help you solve a problem
    15·1 answer
  • What is the area of the triangle shown below ​
    8·2 answers
  • Can someone plz help me with this one problem plz!!!
    15·2 answers
  • Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the dif
    15·1 answer
  • Evaluate<br> for x = 2 and y = -4.<br> 1/2^-2x^-3y^5<br><br> 16<br> -1/32<br> -16<br> -4
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!