If (x + k) is a factor of f(x), which of the following must be true?

Complete Question:

If (x + k) is a factor of f(x), which of the following must be true?

Correct

If (x + k) is a factor of f(x), f(-k)=0 must be true

option B

Step-by-step explanation:

We have , (x + k) is a factor of f(x) . For this case we have a function of the form: . Thus,

x: independent variable

f (x): dependent variable

Since (x + k) is a factor of f (x) then it follows that:

For we have:

⇒

From here, we clear the value of x:

⇒

Then, replacing this value of x in the function, we have:

⇒

Therefore , Correct option B) f (-k) = 0.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: