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
attashe74 [19]
3 years ago
8

What is the complete factorization of the polynomial function over the set of complex numbers? f(x)=x^3+3x^2+16x+48

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

Answer:(x+3)(x+4i)(x-4i)  is the required factorization of f(x).


Step-by-step explanation:

To factor the expression we must first group the terms and then take out common from these groups

f(x)=x^3+3x^2+16x+48=(x^3+3x^2)+(16x+48)

Taking x^2 common from first group and the 16 from second group we get:


f(x) = x^2(x+3)+16(x+3) = (x+3)(x^2+16)


Now, to factor in complex from we have to break term x^2+16


f(x)= (x+3){x^2-(-4i)^2}

As, i^2 = -1 , therefore (-4i)^2 = 16i^2 =-16

Also using identity a^2-b^2 =(a+b)(a-b)

On solving

f(x) = (x+3)(x+4i)(x-4i)

(x+3)(x+4i)(x-4i)  is the required factorization of f(x).


You might be interested in
A line with a slope of 10 passes through the points ( -5, - 9) and ( - 4,a). What is the value of a?
Setler79 [48]
The slope is 10
(-5,-9)
(-4,-a)
a=-19
Because the slope is 10, that means when the input increases, the output will increases 10.
4 0
3 years ago
Sam spends 12.5% of his day doing homework. There are 24 total hours in one day. Which proportion could be used to calculate the
otez555 [7]
Homework =  12.5% of 24 hours  = 0.125 x 24  = 3 hours

Sam spent <u>3 hours</u> on homework.

Proportion of the time spent on homework = 3/24 = 1/8

Answer: Same spent 1/8 of his day on homework.
6 0
2 years ago
Read 2 more answers
alfred deposited $893.78 in a savings account that earns 2.2% simple interest. What is alfreds account balance after seven years
ASHA 777 [7]
Hello!  The formula for finding simple interest is prt. That means multiply the principal (initial amount) by the rate (percentage) by time (months or years). The principal is $893.78 and the interest rate is 2.2%. 893.78 * 2.2% (0.022) is 19.66316. Do not delete that number. The time is 7 years. Now multiply that number by 7 in order to get 137.64212 or $137.64 when rounded to the nearest whole hundredth.  Now, let's add both numbers. 893.78 + 137.64 is 1,031.42. There. Alfred's balance after seven years is $1,031.42.
7 0
3 years ago
What is the equation of this graphed line ?
yanalaym [24]
Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).
7 0
2 years ago
Read 2 more answers
What are the signs of the coordinates of a point in each of the four quadrants
guajiro [1.7K]
On the Cartesian plane in two dimensions, the quadrants are <span>I (+,+), II (−,+), III (−,−), and IV (+,−). The numbering, starting in the upper right corner, goes counter-clockwise.</span>

6 0
2 years ago
Other questions:
  • Kelly bought 3 peppers, 2 onions, and 4 tomatoes.What is the ratio of peppers to all the vegetables Kelly bought
    11·2 answers
  • Find the difference 6x^2-14x+4/x(x-2) - 6x-1/x+1
    5·2 answers
  • The equation y=1/5x represents a proportional relationship. Explain how you can tell the relationship is proportional from the g
    7·1 answer
  • A steel ball whose mass is 2.0 kg is rolling at a rate of 2.8 m/s. What is its momentum?
    6·1 answer
  • Evaluate 6 - 2(-1) + | -5 |
    9·1 answer
  • An automobile went 84 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 126 miles
    15·2 answers
  • Justin is starting his own laundry business. Justin thinks he will do a better job than his competitors, so he thinks he can cha
    14·1 answer
  • This is all I need because its 55% of my grade on this practice, please help ty.
    7·1 answer
  • 7. If y varies jointly with x and z, and y = 24
    8·1 answer
  • Sarah bought snacks for her team's practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!