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
fomenos
3 years ago
12

What is the completely factored form of f(x)=x3+5x2+4x−6?

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
You might be interested in
Geometry! Please help!
Travka [436]
The answer is 315 as the formula is : a+b/2•h.
3 0
3 years ago
Read 2 more answers
Help pls hw 14 and 15 mostly those the rest I’ll do
Olenka [21]

Answer:

Answer 14

Step-by-step explanation:

answer 37.38

3 0
3 years ago
Read 2 more answers
Math math help ASAP
tiny-mole [99]

Answer:

103.67 in³

Step-by-step explanation:

given Volume of cone is 1/3 * π * r² * h

here given r = 6/2 = 3 , height = 11 inch

using the formula = 1/3 * π * 3² * 11

                              =103.67 in³ or 33π in³

7 0
2 years ago
Read 2 more answers
Cal had $15. He spent $3 on pens and $8 on a book.
nikklg [1K]
He spent $11 dollars minus tax
3 0
2 years ago
Read 2 more answers
What is the quotient?<br> 7)<br> 126<br> А.<br> 16<br> B.<br> 17<br> С<br> 18<br> D<br> 19
Hunter-Best [27]

Answer:

C

Step-by-step explanation:

The quotient is 18

6 0
3 years ago
Other questions:
  • An election charges $30 for a service call plus $75 per hour of service.if he changed $210 how many hours did he work?
    11·2 answers
  • What is the value of x?
    5·2 answers
  • PLEASE HELP<br> THANK YOU
    6·1 answer
  • The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 a
    5·1 answer
  • A seamstress is making a decorative pillow and wants to see lace around the trim. The pillow is in the shape of a triangle with
    6·1 answer
  • Solve: 3x-3y=3<br> y=-5x-17
    9·1 answer
  • How do we get x+2=6 from 3x+6=18 solve for x and explain how we get that equation
    7·2 answers
  • Which mathematical figure has length but no beginning or end?
    10·2 answers
  • Twice a number minus 25 is less than 89. Translate it into an inequality and find the solution
    8·1 answer
  • A truck driver drove 80 miles in 1 3/4 hours. What is the speed of the truck in miles per hour?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!