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
matrenka [14]
3 years ago
14

Select all polynomials that have (x – 3) as a factor.

Mathematics
2 answers:
Bumek [7]3 years ago
8 0
<h3>3 Answers: A, C and D</h3>

In other words, everything but choice B

==========================================================

Explanation:

You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division

There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

------------------------------------------------

Here's a fairly short proof:

Consider a polynomial q(x) such that

p(x) = (x-k)q(x)

which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.

If we plug x = k into the p(x) function, we get

p(x) = (x-k)q(x)

p(k) = (k-k)q(k)

p(k) = 0*q(k)

p(k) = 0

------------------------------------------------

How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.

So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.

-------------------------------------------------

Plug x = 3 into the first function

A(x) = x^3 - 2x^2 - 4x + 3

A(3) = 3^3 - 2(3)^2 - 4(3) + 3

A(3) = 0

This shows (x-3) is a factor of the function A(x)

------------------------------------------------

Repeat for the second function

B(x) = x^3 + 3x^2 - 2x - 6

B(3) = 3^3 + 3(3)^2 - 2(3) - 6

B(3) = 42

We don't get an output of 0, so (x-3) cannot be a factor of B(x)

-----------------------------------------------

Now onto the third function

C(x) = x^4 - 2x^3 - 27

C(3) = 3^4 - 2(3)^3 - 27

C(3) = 0

So (x-3) is a factor of C(x)

----------------------------------------------

Finally the last function

D(x) = x^4 - 20x - 21

D(3) = 3^4 - 20(3) - 21

D(3) = 0

Therefore (x-3) is a factor of D(x) as well.

mote1985 [20]3 years ago
4 0

Answers: A, C, D

Explanation: Let (x-3)=0. x then equals 3. Substitute f(3) into each equation, and the ones which equal 0 are the answer.

You might be interested in
Emily rented a bike from kaylas bikes. It cost $15 plus $5 per hour.
crimeas [40]

Answer: 7 hours.

Step-by-step explanation:

The rental price is 15. Add 5 per hour (5x) and the total must be equal to $50

15+5x=50

Solve for x;

5x=50-15\\5x=35\\x=\frac{35}{5}\\ x=7

4 0
3 years ago
Write nine hundred one and seventy-five thousands in expanded form
34kurt
900000+1000+70000+5000
6 0
3 years ago
7. A patient has a urinary tract infection so Dr. Padron prescribes Ancef. A 1200 mL bag contains 400 mg of Ancef. If the patien
liraira [26]

Answer:

  200 mg

Step-by-step explanation:

The dose (d) is proportional to amount of fluid received, so ...

  d/(600 mL) = (400 mg)/(1200 mL)

  d = (600 mL)(400 mg)/(1200 ml)

  d = 200 mg

The patient received 200 mg of drug.

7 0
3 years ago
Help please! Will give brainiest if correct!
frosja888 [35]
Slope is 3/4
You are welcome
4 0
2 years ago
Read 2 more answers
ackie’s report is 5 pages longer than half the number of pages in Kane’s report. There are 14 pages in Kane’s report. How many p
natulia [17]
Jackie's report is 12 pages long.
4 0
3 years ago
Other questions:
  • Most _____ jobs are worked 10 to 20 hours per week.
    5·1 answer
  • Savannah is having her teammates over after the basketball game. She decided that 2 pizzas would feed 5 people, so how many pizz
    5·1 answer
  • The sum of three consecutive numbers is 144. What is the smallest of the three numbers ?
    8·2 answers
  • CAN SOMEONE LOOK AT MY QUESTIONS I NEED HELP ASAP I JUST ASKED A QUESTION YESTERDAY ND I NEED HELP . JUST GO LOOK AT MY QUESTION
    15·1 answer
  • Help please I’ll mark as brainliest!
    9·1 answer
  • What is the slope of a line parallel to the line whose equation is x-3y=-27 Fully reduce your answer​
    8·1 answer
  • Expand 2x(5x-2)<br><br> PLEASEEEEEEEE!!!!!!!!!!!!
    8·2 answers
  • HELP PLS ASAP!!!
    15·2 answers
  • Here is a graph of a quadratic function f(x). What is the minimum value (y-value only) of f(x)?
    5·1 answer
  • Can somebody help me with the write
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!