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charle [14.2K]
3 years ago
8

Use the remainder theorem to find which of the following is NOT a factor of x^3 – 4x^2 – 4x + 16.

Mathematics
1 answer:
nataly862011 [7]3 years ago
3 0

Answer: x - 12 is not a factor.

Step-by-step explanation:

The equation

x³ - 4x² - 4x + 16

To know which of the following is a factor , we continue to find the value of x and substitute into the equation and see the one that gives zero. The one that gives zero is the factor.

(a) x + 2

If x + 2 = 0

x = -2, now substitute for x in the equation and find out if it will be zero.

x³ - 4x² - 4x + 16 = (-2)³ - 4(-2)² - 4(-2) + 16.

= -8 - 16 + 8 + 16

= 0.

Therefore, x + 2 is a factor.

(b) x - 12

If x - 12 = 0, then x = 12

x³ - 4x² - 4x + 16

(12)³ - 4(12)² - 4(12) + 16

1728 - 576 - 48 + 16

= 1,120 , not a factor.

(c) x - 2

If x - 2 = 0, then x = 2

x³ - 4x² - 4x + 16

(2)³ - 4(2)² - 4(2) + 16

8 - 16 - 8 + 16

= 0, Therefore, x - 2 is a factor.

(d) x - 4

If x - 4 = 0, x = 4

x³ - 4x² - 4x + 16

(4)³ - 4(4)² - 4(4) + 16

48 - 48 - 16 + 16

= 0,therefore, x - 4 is also a factor.

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If nine is X percent of 45, what is X percent of 5
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Answer:

x percent of 5 is 1

Step-by-step explanation:

Nine is x percent of 45

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5 0
3 years ago
A plane flies 720 miles with the wind in 3 hours. The return trip against the wind takes 4 hours. What is the speed of the wind
Mandarinka [93]
Let p and w represent the speed of the plane and the speed of the wind, respectively.
.. speed = distance/time
.. p +w = 720/3 = 240
.. p -w = 720/4 = 180

Add the two equations to eliminate w.
.. 2p = 420
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4 0
3 years ago
If
UkoKoshka [18]

Answer:

-8n + 9

Step-by-step explanation:

Given that,

A = -3n + 2

B = 5n - 7

Before solving you have to know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Let us solve now.

A - B

-3n + 2 -(5n - 7)

-3n + 2 - 5n + 7

Combine like terms

-3n - 5n + 2 + 7

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Hope this helps you.

Let me know if you have any other questions :-)

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