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
baherus [9]
3 years ago
11

What is the completely factored form of f(x)=x^3-7x^2+2x+4

Mathematics
1 answer:
xxMikexx [17]3 years ago
8 0

Solution, \mathrm{Factor}\:x^3-7x^2+2x+4:\quad \left(x-1\right)\left(x^2-6x-4\right)

Steps:

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

Use\:the\:rational\:root\:theorem,\\a_0=4,\:\quad a_n=1,\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1},\\\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-1,\\\left(x-1\right)\frac{x^3-7x^2+2x+4}{x-1}

\frac{x^3-7x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{x^3-7x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}x^3-7x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{x^3}{x},\\\mathrm{Quotient}=x^2,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}x^2:\:x^3-x^2,\\\mathrm{Subtract\:}x^3-x^2\mathrm{\:from\:}x^3-7x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-6x^2+2x+4,\\Therefore,\\\frac{x^3-7x^2+2x+4}{x-1}=x^2+\frac{-6x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{-6x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-6x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-6x^2}{x}=-6x,\\\mathrm{Quotient}=-6x,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-6x:\:-6x^2+6x,\\\mathrm{Subtract\:}-6x^2+6x\mathrm{\:from\:}-6x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-4x+4,\\\mathrm{Therefore},\\\frac{-6x^2+2x+4}{x-1}=-6x+\frac{-4x+4}{x-1}

\mathrm{Divide}\:\frac{-4x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-4x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-4x}{x}=-4,\\\mathrm{Quotient}=-4,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-4:\:-4x+4,\\\mathrm{Subtract\:}-4x+4\mathrm{\:from\:}-4x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=0,\\\mathrm{Therefore},\\\frac{-4x+4}{x-1}=-4

\mathrm{The\:Correct\:Answer\:is\:\left(x-1\right)\left(x^2-6x-4\right)}

\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

You might be interested in
6) 8x + 38 =-34-6 - 4x)​
nlexa [21]

Answer:

-6.5 would be your answer

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
If a= (3/6) and b=(-3/-5) find-3a+4b
iren2701 [21]

Answer:

-3a + 4b

= -3(3/6) + 4(-3/-5)

= -3/2 + 12/5

= 9/10

3 0
3 years ago
2. During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For
Luda [366]

Answer:

The piecewise equation is given as :A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\  75& \text{ if } 3

Step-by-step explanation:

Let x be the time in hour and A(x) be the amount of accumulating rainfall at time x.

We are given that in the first three hours the rain fell at a constant rate of 25mm per  hour

Amount of rainfall in 1 hour = 25

Amount of rainfall in t hours = 25x

A(x) = 25x ; 0 \leq x \leq 3

The rain then slows down and remains constant

So, Amount of rain for that hour = 25 \times 3 = 75 mm

75 mm ; 3

Now we are given that started again at a constant rate of 20 mm  per hour for the next two hours.

Amount of rain after 4 hours = 75+20(x-4) ; 4 \leq x\leq 6

The rain increases at a rate of 20t from 4 ≤ x ≤ 6.

Hence the piecewise equation is given as :A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\  75& \text{ if } 3

7 0
3 years ago
 death valley located in the United States is 282 feet below sea level is the level of Galilee located in Israel is 682 feet be
umka21 [38]

Answer:

400 feet.

Explanation:

We need to find the difference between the lowest point of Galilee and the lowest point of Death Valley. We can find this by subtracting the lowest point of Galilee by the lowest point of Death Valley. It says the lowest point of Galilee is 682 feet below sea level and the lowest point of Death Valley is 282 feet below sea level. Therefore, we subtract 682 - 282, which equals 400.

3 0
3 years ago
Write the fractions in order greatest to least. 1/2, 1/4, 1/3
Lelechka [254]
Firts1/2,
2) 1/3,
3) 1/4
4 0
3 years ago
Read 2 more answers
Other questions:
  • how many ounces of a 12 alcohol solution must be mixed with 6 ounces of a 20% alcohol solution to make a 16% alcohol solution?
    5·1 answer
  • Which number is equivalent to the fraction 15 over 7?
    10·1 answer
  • How do I simplify this?
    12·2 answers
  • How many solutions does the following equation have? <br><br> 3(2+x)=3x+2=
    5·1 answer
  • If x is greater than 6, then -7 is a solution true or false
    11·1 answer
  • A mini-cone has a diameter of 3 inches and holds 10 in3 of ice cream. A mega-cone holds 49.13 in3 of ice cream. If the cones hav
    12·1 answer
  • The midpoint of XY is point M (-12,5) if the coordinates of x are (3,-3) what are the coordinates pf y
    12·1 answer
  • Do not really understand this question anybody help ?
    8·1 answer
  • Multiple choice geometry help trig ?!!!!!!!!
    12·1 answer
  • What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!