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
Bad White [126]
2 years ago
8

P(x)= 3x^3-5x^2-14x-4

Mathematics
1 answer:
nexus9112 [7]2 years ago
7 0
   
\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\


\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)


\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm  \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm  \sqrt{4+16}}{2}=\frac{2\pm  \sqrt{20}}{2}=\frac{2\pm  2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}



You might be interested in
3.84761 to 3 decimal place
yKpoI14uk [10]
The answer is 3.848.
3 0
2 years ago
Answer ASAP PLS -
Talja [164]
TQV: 50
good luck :’)
3 0
2 years ago
The clownfish kay wanted to buy for $12 last week has been marked up 8%. What is the new price of the fish?
Crank
The markup is 8%, meaning it costs 8% more.
The starting price is 100%.
Therefore, the markup is 108% of $12.
If we multiply 12 by 108% (1.08), we will get our answer of $12.96
4 0
3 years ago
Read 2 more answers
All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weigh
BaLLatris [955]

Answer:

The largest possible weight of flour is 11.25  pounds.

Step-by-step explanation:

To start with, we will assume that the weight of 1 sack of sugar = x pounds

We will also assume that the weight of 1 sack of flour = y pounds

So, the weight of 2 sacks of sugar = 2 * (x) = 2x

Same thing goes for the weight of 3 sacks of flour  = 3 * (y) = 3y

Supposing that the weight of (2 sacks of sugar + 3 sacks of flour) ≤ 40 pounds

= 2x + 3y ≤ 40............ we'll call that equation 1.

Also, suppose that the weight of ( 1 sack of flour) ≤ 2 sacks of sugar + 5 pounds

= y ≤ 2x + 5........................ we'll call that equation 2

Therefore, we'll solve for the values of x and y in the two equations and we will get:

2x + 3y ≤ 40

y ≤  2x + 5

Now, substitute the value of y into equation 1

2x + 3y ≤ 40 ⇒ 2x + 3(2x +5) =40

⇒ 2x + 6x + 15= 40

⇒ 8x + 15 = 40

⇒ 8x = 25

⇒ x = 25/8

⇒ x = 3.12

x cannot be more than 3.12 pounds, so we solve for y

Putting the value of x into equation 2, we'll get

⇒ 2y + 5 = 2(3.12) + 5

⇒ y = 11.25 pounds.

So, n cannot be more than 11.25 pounds

8 0
3 years ago
8/3 × (−2 1/2) = ?<br><br><br>Thanks!
Veronika [31]

Answer: -20/3

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve: 9^8-x= 27^x-3
    14·1 answer
  • Kevin has 32 golf balls. He puts the same number of golf balls into 8 bags. how many are in each bag
    7·2 answers
  • What is the value of x in the equation x – y = 30, when y = 15?
    7·2 answers
  • What type of parent function does the equation f (x) = 1/x
    13·1 answer
  • What is 20 over 3 divided into its simplest form?
    15·1 answer
  • Who now that I do now is cus I am in 5 grade
    13·1 answer
  • A leaky toilet in Mr. Walker's house increases his water bill by $2.14 each day. The toilet leaks for 19 days in April and all 3
    14·1 answer
  • What is the measure of S?
    7·1 answer
  • Pre college need help with this question
    15·1 answer
  • If x +3.5 =14.25 then how can i find x
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!