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VikaD [51]
3 years ago
10

Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

Mathematics
2 answers:
ollegr [7]3 years ago
3 0

Answer:

f(4)=0


Step-by-step explanation:

<em>The </em><em>Remainder Theorem</em><em> states that when you divide a polynomial f(x)  by a linear factor  (x-a) , where a  is a constant, the remainder is f(x)  evaluated at x=a</em>

<em>Moreover, according to the </em><em>Factor Theorem</em><em>, an extension of the Remainder Theorem, if the remainder of the function f(x) is </em><em>0</em><em> when evaluated at x=a , then (x-a)  is said to be a factor of the polynomial f(x)</em>

Given the 2 theorems above, it follows that if (x-4)  is a factor of f(x) , then the remainder is equal to 0 when f(x) is evaluated at x=4

Which means f(4)=0

Third answer choice is correct.


Ksivusya [100]3 years ago
3 0
If x-a is the factor of f(x) then
f(a) = 0

Hence,
if x-4 is a factor of f(x) then f(4) = 0

option C
You might be interested in
X²+x=0<br> x³-25x=0<br> x²=4x<br> 4x²-4x=1
-BARSIC- [3]

Answer:

x²+ x = 0

x ( x +1 ) = 0

x = -1

x³-25x=0

x ( x² - 25 ) = 0

x² = 25

x = 5

x²=4x

x² - 4x = 0

x ( x- 4 ) = 0

x = 4

4x²-4x=1

4x²-4x - 1 = 0

4 x² - 2x - 2x - 1 = 0

2x ( 2x - 1 ) - 1 ( 2x- 1 ) = 0

2x- 1 ) ² = 0

2x = 1

x = 1/ 2

mark me as brainliest

7 0
3 years ago
The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 at exactly one point. What is k? Thank you! :)
bearhunter [10]

Answer:

49/8 is the value of k

Step-by-step explanation:

We have the system

x = -2y^2 - 3y + 5

x=k

We want to find k such that the system intersects once.

If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.

This equation has one solution when it's discriminant is 0.

Let's first rewrite the equation in standard form.

Subtracting k on both sides gives

0=-2y^2-3y+5-k

The discriminant can be found by evaluating

b^2-4ac.

Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that

a=-2, b=-3, and c=5-k.

So we want to solve the following equation for k:

(-3)^2-4(-2)(5-k)=0

9+8(5-k)=0

Distribute:

9+40-8k=0

49-8k=0

Add 8k on both sides:

49=8k

Divide both sides by 8"

49/8=k

6 0
3 years ago
Analysis of an accident scene indicates a car was traveling at a velocity of 69.5 mph (31.1 m/s) along the positive x-axis at th
STatiana [176]

We can find the acceleration via

{v_f}^2-{v_i}^2=2a\Delta x

We have

\left(5.20\dfrac{\rm m}{\rm s}\right)^2-\left(31.1\dfrac{\rm m}{\rm s}\right)^2=2a(115\,\mathrm m)

\implies\boxed{a=-4.09\dfrac{\rm m}{\mathrm s^2}}

Then by definition of average acceleration,

a_{\rm ave}=\dfrac{v_f-v_i}t

so that

-4.09\dfrac{\rm m}{\mathrm s^2}=\dfrac{5.20\frac{\rm m}{\rm s}-31.1\frac{\rm m}{\rm s}}t

\implies\boxed{t=6.33\,\mathrm s}

We alternatively could have found the time without knowing the acceleration. Since acceleration is constant, the average velocity is

v_{\rm ave}=\dfrac{x_f-x_i}t=\dfrac{v_f+v_i}2

Then

\dfrac{115\,\rm m}t=\dfrac{5.20\frac{\rm m}{\rm s}+31.1\frac{\rm m}{\rm s}}2

\implies\boxed{t=6.33\,\mathrm s}

7 0
3 years ago
An element with a mass of 630 grams decays by 30% per minute. To the nearest minute, how long will it be untill there are 30 gra
nataly862011 [7]

Answer:

It should take somewhere between 8 to 9 minutes to decay until there are 30 grams remaining.

6 0
3 years ago
Tyce hit 3/5 of the baseballs pitched to him during batting practice.Mason hit 3/4 of the number of the pitched that tyce hit. w
marissa [1.9K]

Answer: 9/20

Step-by-step explanation:

From the question, we are informed that Tyce hit 3/5 of the baseballs pitched to him during batting practice and that Mason hit 3/4 of the number of the pitched that tyce hit.

The fraction of pitches that Mason hit will be gotten by multiplying 3/4 by 3/5 This will be:

= 3/4 × 3/5

= 9/20

6 0
3 years ago
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