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
Andrews [41]
3 years ago
9

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
7 0
The function is: f ( x ) = x³ - 2 x² - 68 x - 120
If f ( - 2 ) = 0, we have to divide this equation by: ( x + 2 )
( x³ - 2 x² - 68 x - 120 ) : ( x + 2 ) = x² - 4 x - 60
- x³ - 2 x²
--------------
       - 4 x² - 68 x - 120
         4 x² + 8 x
  ---------------------------
                - 60 x - 120
                  60 x + 120
                -----------------
                               0
After that for a function: f ( x ) = x² - 4 x - 60;   f (  - 6 ) = 0
( x² - 4 x - 60 ) : ( x + 6 ) = x - 10
 -x² - 6 x
-----------------
        - 10 x - 60
          10 x + 60
          -------------
                      0
Answer:
       C )    ( x - 10 ) ( x + 2 ) ( x + 6 )
 
You might be interested in
​(6x2−2x+16​)+​(4x2+7x−55​)
AysviL [449]
(6 • 2 - 2x + 16) + (4 • 2 + 7x - 55)
(-2x + 16 + 6 • 2) + (7x - 55 + 4 • 2)
(-2x + 16 + 12) + (7x - 55 + 8)
-2x + 28 + 7x - 47
-2x + 7x + 28 - 47
5x + (-19)
5x - 19
So the answer is 5x - 19.

8 0
3 years ago
3 and 7/10 x 4 and 4/5<br> Please help<br> I want to now if my answer is correct
BabaBlast [244]
The answer is 17 and 19/25
3 0
3 years ago
Help me, please lol i really need help
yan [13]

Answer:

honestly I THINK it's the first one

4 0
3 years ago
2. You are given the hyperbolic relation modeled by xy = -2. Do the following: a) Rewrite the relation such that the dependent v
N76 [4]

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

The given equation is :

  • xy =  - 2

1. The relationship such that dependent variable (y) is isolated is :

  • y =   \dfrac{ - 2}{x}

2. The table accompanying this equation :

  • x = -4 and y = 0.5

  • x = -1 and y = 2

  • x = - 0.5 and y = 4

  • x = 0 and y = undefined

  • x = 0.5 and y = -4

  • x = 1 and y = -2

  • x = 4 and y = -0.5

3. graph of the given equation is in attachment ~

4 0
3 years ago
Part 1
svetlana [45]

Answer:

A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.

B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.

Step-by-step explanation:

f(x) = 12x^2 + 5x - 2.

Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).

To find the roots of f(x), set f(x) = 0. Therefore:

12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:

12x^2 + 8x - 3x - 2 = 0.

4x(3x + 2) -1(3x+2) = 0.

(4x-1)(3x+2) = 0.

4x-1 = 0 or 3x+2 = 0.

x = 1/4 or x = -2/3.

It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!

8 0
3 years ago
Other questions:
  • Following a translation, the measures of the angles in a pre-image _____.
    12·2 answers
  • The Pythagorean Theorem ONLY works on which triangle?​
    15·2 answers
  • Solve the system of linear equations by substitution. 11x−7y=−14 x−2y=−4
    8·1 answer
  • Write an equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilib
    5·1 answer
  • X+2y=7 <br> 3x-2y=-3 solving systems by substitution
    7·1 answer
  • So I have 5 cats and eat 2819 how many do I have left
    7·2 answers
  • A- 15 √11<br> B- 30 √22<br> C- 30 √11<br> D- 15 √22
    12·2 answers
  • HELPPPPPP ASAPPPPP PLS
    15·1 answer
  • Question 1 (10 points) What is the sum of two fractions: 3/4 + 1/6​
    10·1 answer
  • Help plz:)!!!!!!!!!!!!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!