MATHEMATICS HIGH SCHOOL

What is the factored form of 125x6 – 8?(5x2 – 2)(25x4 – 10x2 – 4)
(5x2 – 2)(25x4 – 10x2 + 4)
(5x2 – 2)(25x4 + 10x2 + 4)
(5x2 – 2)(25x4 + 10x2 – 4)

Answers

Answer 1
Answer:

Answer:

(5x^2-2)(25x^4 +10x^2+4)

Step-by-step explanation:

125x^6 – 8

We write the numbers in exponential form

125= 5*5*5 = 5^3

8 = 2*2*2= 2^3

Now 125x^6 - 8 becomes 5^3x^6 - 3^3

5^3x^2*3- 3^3

(5x^2)^3 - 2^3

We got the expression in cube form a^3- b^3= (a-b)(a^2+ab+b^2)

(5x^2)^3 - 2^3

a= 5x^2  and b= 2

(5x^2)^3 - 2^3=(5x^2-2)((5x^2)^2- 5x^2 * 2+ 2^2)

=(5x^2-2)(25x^4 +10x^2+4)
Answer 2
Answer:

The factored form of 125x⁶ - 8 is (5x² - 2)(25x⁴ + 10x² + 4). This expression is obtained by applying the difference of squares formula and then factoring the difference of cubes further.

To factor the expression 125x⁶ - 8, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b).

Step 1: Recognize that 125x⁶ can be expressed as (5x^2)³ and 8 can be expressed as (2)³.

Step 2: Apply the difference of squares formula:

125x⁶ - 8 = (5x²)³ - (2)³

Step 3: Now we have a difference of cubes, so we can factor it as:

125x⁶ - 8 = (5x² - 2)((5x²)² + 5x² * 2 + 2²)

Step 4: Simplify the second part of the expression:

125x⁶ - 8 = (5x² - 2)(25x⁴ + 10x² + 4)

Therefore, the factored form of 125x⁶ - 8 is (5x² - 2)(25x⁴ + 10x² + 4). This expression is obtained by applying the difference of squares formula and then factoring the difference of cubes further.

To know more about factored form:

brainly.com/question/33784635


#SPJ6

Related Questions

How can I graph y=1000(1+.0925/12)^m
The sum of the measures of the interior angles of a polygon is 2880°. How many sides does the polygon have?14161820
2.46875 in fractionform
If x = 3 units, y = 13 units, and h = 7 units, then what is the area of the trapezoid shown above?
Expand or condense the following expression: 3log_2y+log_25-log_2 10

One container holds 1 1/7 quarts of water and second container holds 5 3/4 quarts of water how many more harts of water does the second container hold then the first

Answers

Answer:

129/28 (4.6 approx.)

Step-by-step explanation:

The first hols 1 1/7 quarts, it is: 1 + 1/7

Using 7 as common denominator and summing:

1 + 1/7 = 7/7 + 1/7 = 8/7

The second holds 5 3/4 which is: 5 + 3/4. Using 4 as common denominator:

5 + 3/4 = 20/4 + 3/4 = 23/4

Now we need to know how much greater is 23/4 than 8/7. For comparing them we need to set them to a common denominator. The easiest way is use a number that is multiple of both, 4 and 7, lets us 28. We need to multiply the numerators by the number that, multiplied by denominators gives us 28. For the first is 4, and for the second 7.

8/7 = (8*4)/7*4=32/28

23/4= (23*7)/4*7 = 161/28

Now, we only have to subtract:

23/4 - 8/7 = 161/28 - 32/28 = 129/28

So, the second container has 129/28 more quarts of water (approx. 4.60) than the first.

Based on the graph below, what are the solutions to the equation f(x) = g(x)?graph of function f of x equals 5 times x minus 2. Graph of function g of x equals x cubed minus 2 times x squared minus x plus 2

(A)x = −3.7, 0.5, 3.4
(B)x = −1, 1, 2
(C)x = −2, 2, 3
(D)x = −2, 0.6, 3.4

Answers

Answer:

The answer is the option D

x=-2,0.6,3.4

Step-by-step explanation:

we have

f(x)=5x-2

g(x)=x^(3)-2x^(2)-x+2

To solve the system of equations equate f(x) and g(x)

f(x)=g(x)

The solution of the system of equations is the intersection points both graphs

Using a graphing tool

see the attached figure

The solutions of x are

x=-2,0.6,3.4

The  solutions to the equation f(x) = g(x) is −2, 0.6, 3.4.

The correct option is (A)

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

given:

f(x)= 5x-2

g(x)= x³-2x²-x+2

Now, equate f(x)= g(x)

The solution is shown using graphical method.

By looking the graph, the graph of function g(x) touches the line f(x) at three point −2, 0.6, 3.4.

Hence, the solution of x will be −2, 0.6, 3.4.

Learn more about function here:

brainly.com/question/12719286

#SPJ5

Im thinking of a number , multiply it by 4 and add 5 to the product, you get 41. Find the numbera) 9
b) 10
c) 11
d) 12

Answers

A

I hope this helps:D

Answer:

Answer is a) 9

Step-by-step explanation:

9 x 4 = 36

36 + 5 =41

Hope this help (｡･ω･｡)

Edit:

or you can use this method

41 - 5 = 36

36 divides by 4, then you will get 9

Solve the compound inequality. Graph the solution
-2 ≤ 2x – 4 < 4

Answers

-2 \ \textless \ = 2x - 4 \ \textless \ 4 

-2+4\ \textless \ 2x\ \textless \ 4+4  Add \ 4 \ to \ the \ whole \ equation 

2\ \textless \ 2x\ \textless \ 8  Simplify \ inequality 

1\ \textless \ x\ \textless \ (8)/(2) Divide \ the \ whole \ equation \ by \ 2 

1\ \textless \ x\ \textless \ 4 = (1,4)

Five eighths added to Q number is 4. Determine the number.

Answers

Yes five eights added to Q is 4!

If f(c) = 0, which of the following statements must be true?A. The point (c,0) lies on the graph of f(x)
B. x - c is a factor of f(x).
C. c is a 0 for f(x).
D. All three statements are true.

Answers

For this case suppose we have a function of the form:

y = f (x)

Where,

x: independent variable

y: dependent variable

We have then that the value of the function for x = c is:

f (c) = 0

Therefore, we have that:

The point (c, 0) belongs to f (x)

x-c is a common factor of f (x) because the function evaluated at x = c is equal to zero.

x = c is a root of f (x) so c is a zero of the function f (x)

Answer:

D. All three statements are true.
Answer: D) All three statements are true.
Thank you.
Other Questions
A motorcycle travels 62 miles in twohours. At this rate, how many miles willthe motorcycle travel in 3 hours?
Taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. Provide Taylor some feedback that explains which part of her answer is incorrect and why it is incorrect. f(x)=2x+1g(x)=2x^2+1
Which amount is less 250 mL or 250 L
The Halloween candy bowl of chocolates had 80 pieces of candy. On average 3 pieces were eaten every hour.The bowl of sour candy had 120 pieces and 5 pieces were eaten each hour.Write and solve the system. Write each equation in the order that it appears in the problem.At what hour will the bowls have the same amount? How many pieces will each bowl have at this hour?