We appreciate your visit to Resolve into factors 12 tex 4x 4 81 tex 13 tex 9x 4 3x 2 1 tex 14 tex x 4 x 2 1 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's resolve each of these expressions into their factors step-by-step:
12. Factor [tex]\( 4x^4 + 81 \)[/tex]:
This is a sum of squares, which typically does not factor into simple real factors. However, it can be expressed as a product of two factors over complex numbers. In our case, the expression can be factored into:
[tex]\[
(2x^2 - 6x + 9)(2x^2 + 6x + 9)
\][/tex]
This form uses complex roots due to the sum of squares structure.
13. Factor [tex]\( 9x^4 - 3x^2 + 1 \)[/tex]:
This is a quadratic in terms of [tex]\( x^2 \)[/tex]. Here, you consider [tex]\( x^2 \)[/tex] as a single variable and factor the expression:
[tex]\[
(3x^2 - 3x + 1)(3x^2 + 3x + 1)
\][/tex]
Each factor here forms a quadratic trinomial.
14. Factor [tex]\( x^4 + x^2 + 1 \)[/tex]:
This expression is a particular form of polynomial that factors as follows:
[tex]\[
(x^2 - x + 1)(x^2 + x + 1)
\][/tex]
Notice that each factor is a quadratic and contains the variable [tex]\( x \)[/tex].
15. Factor [tex]\( x^4 + 3x^2y^2 + 4y^4 \)[/tex]:
This expression appears to be a form of a quadratic in [tex]\( x^2 \)[/tex] and [tex]\( y^2 \)[/tex]. It can be factored as:
[tex]\[
(x^2 - xy + 2y^2)(x^2 + xy + 2y^2)
\][/tex]
Each factor highlights the mixed terms and maintains the symmetry in the powers of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
These factored forms show how the given polynomials can be broken into products of simpler expressions.
12. Factor [tex]\( 4x^4 + 81 \)[/tex]:
This is a sum of squares, which typically does not factor into simple real factors. However, it can be expressed as a product of two factors over complex numbers. In our case, the expression can be factored into:
[tex]\[
(2x^2 - 6x + 9)(2x^2 + 6x + 9)
\][/tex]
This form uses complex roots due to the sum of squares structure.
13. Factor [tex]\( 9x^4 - 3x^2 + 1 \)[/tex]:
This is a quadratic in terms of [tex]\( x^2 \)[/tex]. Here, you consider [tex]\( x^2 \)[/tex] as a single variable and factor the expression:
[tex]\[
(3x^2 - 3x + 1)(3x^2 + 3x + 1)
\][/tex]
Each factor here forms a quadratic trinomial.
14. Factor [tex]\( x^4 + x^2 + 1 \)[/tex]:
This expression is a particular form of polynomial that factors as follows:
[tex]\[
(x^2 - x + 1)(x^2 + x + 1)
\][/tex]
Notice that each factor is a quadratic and contains the variable [tex]\( x \)[/tex].
15. Factor [tex]\( x^4 + 3x^2y^2 + 4y^4 \)[/tex]:
This expression appears to be a form of a quadratic in [tex]\( x^2 \)[/tex] and [tex]\( y^2 \)[/tex]. It can be factored as:
[tex]\[
(x^2 - xy + 2y^2)(x^2 + xy + 2y^2)
\][/tex]
Each factor highlights the mixed terms and maintains the symmetry in the powers of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
These factored forms show how the given polynomials can be broken into products of simpler expressions.
Thanks for taking the time to read Resolve into factors 12 tex 4x 4 81 tex 13 tex 9x 4 3x 2 1 tex 14 tex x 4 x 2 1 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
