Thank you for visiting Completely factor tex f x 256x 4 625 tex. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To factor the polynomial [tex]\( f(x) = 256x^4 - 625 \)[/tex], we first recognize that it is a difference of squares. The expression can be rewritten as:
[tex]\[ f(x) = (16x^2)^2 - 25^2 \][/tex]
This is a difference of squares and can be factored using the formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex]. Here, [tex]\( a = 16x^2 \)[/tex] and [tex]\( b = 25 \)[/tex]. Applying the formula gives:
[tex]\[ f(x) = (16x^2 - 25)(16x^2 + 25) \][/tex]
The first term, [tex]\( 16x^2 - 25 \)[/tex], can also be further factored since it itself is a difference of squares:
[tex]\[ 16x^2 - 25 = (4x)^2 - 5^2 = (4x - 5)(4x + 5) \][/tex]
So, the completely factored form of the original polynomial is:
[tex]\[ f(x) = (4x - 5)(4x + 5)(16x^2 + 25) \][/tex]
Thus, the polynomial [tex]\( f(x) = 256x^4 - 625 \)[/tex] factors into [tex]\((4x - 5)(4x + 5)(16x^2 + 25)\)[/tex].
[tex]\[ f(x) = (16x^2)^2 - 25^2 \][/tex]
This is a difference of squares and can be factored using the formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex]. Here, [tex]\( a = 16x^2 \)[/tex] and [tex]\( b = 25 \)[/tex]. Applying the formula gives:
[tex]\[ f(x) = (16x^2 - 25)(16x^2 + 25) \][/tex]
The first term, [tex]\( 16x^2 - 25 \)[/tex], can also be further factored since it itself is a difference of squares:
[tex]\[ 16x^2 - 25 = (4x)^2 - 5^2 = (4x - 5)(4x + 5) \][/tex]
So, the completely factored form of the original polynomial is:
[tex]\[ f(x) = (4x - 5)(4x + 5)(16x^2 + 25) \][/tex]
Thus, the polynomial [tex]\( f(x) = 256x^4 - 625 \)[/tex] factors into [tex]\((4x - 5)(4x + 5)(16x^2 + 25)\)[/tex].
Thank you for reading the article Completely factor tex f x 256x 4 625 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
