Answer :
To write the given polynomials in ascending order of [tex]x[/tex], we need to reorder the terms starting from the term with the lowest power of [tex]x[/tex] to the highest power.
Let's look at both given polynomials:
Polynomial (a): [tex]2x^4 - 3x^2 + 5 - x^6[/tex]
To rearrange this polynomial:
- The constant term is [tex]5[/tex], which has the lowest power of [tex]x[/tex], essentially [tex]x^0[/tex].
- The next term in order of increasing power is [tex]-3x^2[/tex].
- Then we have [tex]2x^4[/tex].
- The highest power term is [tex]-x^6[/tex].
Thus, in ascending order of [tex]x[/tex], the polynomial is:
[tex]5 - 3x^2 + 2x^4 - x^6[/tex]
Polynomial (b): [tex]12x^4 - 3x^2 + 25 - x^6[/tex]
To rearrange this polynomial:
- The constant term is [tex]25[/tex], again [tex]x^0[/tex].
- The next term in order of increasing power is [tex]-3x^2[/tex].
- Then [tex]12x^4[/tex].
- The highest power term is [tex]-x^6[/tex].
Thus, in ascending order of [tex]x[/tex], the polynomial is:
[tex]25 - 3x^2 + 12x^4 - x^6[/tex]
So, the rewritten polynomials in ascending order of [tex]x[/tex] are:
(a) [tex]5 - 3x^2 + 2x^4 - x^6[/tex]
(b) [tex]25 - 3x^2 + 12x^4 - x^6[/tex]
