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
What is the easiest to understand formula for solving 30 60 90 special right triangles?
Marianna [84]

Step-by-step explanation:

30°, 60°, 90° triangle theorem states that:

Lengths of the side opposite to 60° angle is equal to root 3 upon two times of the length of hypotenuse and side opposite to 30° angle is equal to 1 upon two times of the length of hypotenuse.

Mathematically it can be expressed as:

Length \: of \: sides \: opposite \: to \: 60 \degree \: \\  angle \\  =  \frac{ \sqrt{3} }{ {2} }  \times length \: of \: hypotenuse.\\\\Length \: of \: sides \: opposite \: to \: 30 \degree \: \\  angle \\  =  \frac{1}{ {2} }  \times length \: of \: hypotenuse.\\\\

7 0
2 years ago
How long is the arc intersected by a central angle of startfraction pi over 2 endfraction radians in a circle with a radius of 4
Nimfa-mama [501]

<u>7.1 cm  long is the arc</u><u> intersected by a central angle .</u>

What is length of an arc?

  • The arc length of a circle can be calculated with the radius and central angle using the arc length formula.
  • Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ is in degree.

Given,

Central angle = π / 2

radius = 4.5 cm

we apply formula of length of arc.

length of the arc = angle ×  radius

                              = (π/2) × (4.5 cm)

Now put value of π = 3.14

length of the arc = (3.14 / 2) × (4.5) cm

                            = 7.065 cm ≈ 7.1 cm

Therefore, 7.1 cm  long is the arc intersected by a central angle .

Learn more about<u> </u> length of an arc

brainly.com/question/16991078

#SPJ4

7 0
1 year ago
Factorise fully 21x² +25x =4​
Vitek1552 [10]
X= 1/7, -4/3
________
6 0
2 years ago
Solving an equation involving complementary or supplementary angles! Please help I really would appreciate it
Schach [20]
2x + x + 33 = 90
3x + 33 = 90
3x = 57
x = 19
Angle 1 = 38°
Angle 2 = 52°
8 0
3 years ago
Can you identify these numbers as rational or irrational. Please explain.<br><br> -√127 and 291.87
irina [24]
An irrational number/value is one you cannot express in terms of a ration, or a fraction, it cannot be written as fraction

now 291.87... is simple, two decimals, so you use two zeros at the botom and end up with \bf \cfrac{29187}{100} and boom, there you are, a fraction, nice and dandy

now, let's see the first one -√(127)  well, low and behold, 127 is a prime number, and and thus is has no two factors that'd serve as root, so, there's no rational root that'd give that, that makes it irrational
8 0
3 years ago
Other questions:
  • Find the y value for point F such that DF and EF form a 1:3 ratio. (5 points) Segment DE is shown. D is at negative 3, negative
    14·2 answers
  • Mags is 2 years older than vector. Which equation will help you find mags’ age m if you know vectors age
    15·1 answer
  • What is 345876x 23570746
    5·1 answer
  • Is there any real number exactly one less than its cube intermediate value theorem?
    10·1 answer
  • 7n-(4n-3) simply to create a equivalent expression?
    6·1 answer
  • What is the missing value?
    15·1 answer
  • Which zero has an odd multiplicity?
    12·2 answers
  • Find the area of the triangle.
    12·2 answers
  • Find the value of x. <br> Answer choices<br> 4 4/5<br> 3 1/3<br> 4 2/3<br> 3 2/3
    8·1 answer
  • Answers for both boxes please ​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!