Answer :
Sure! Let's arrange the terms in each polynomial in descending order of the powers of [tex]\( x \)[/tex].
1. For polynomial 22:
[tex]\(-6x + x^4 + 2x^3 - 10\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^4 \)[/tex], [tex]\( x^3 \)[/tex], [tex]\( x^1 \)[/tex] (for [tex]\(-6x\)[/tex]), and [tex]\( x^0 \)[/tex] (for [tex]\(-10\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x^4 + 2x^3 - 6x - 10
\][/tex]
2. For polynomial 23:
[tex]\(0.2mx^4 - 1.3x^5 + 0.4m^2 + 2.1x^3\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^5 \)[/tex], [tex]\( x^4 \)[/tex], [tex]\( x^3 \)[/tex], and [tex]\( x^0 \)[/tex] (for [tex]\(0.4m^2\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
-1.3x^5 + 0.2mx^4 + 2.1x^3 + 0.4m^2
\][/tex]
3. For polynomial 24:
[tex]\(4b + \frac{2}{3}bx + b^3x^2 + x^4\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^4 \)[/tex], [tex]\( x^2 \)[/tex], [tex]\( x^1 \)[/tex] (for [tex]\(\frac{2}{3}bx\)[/tex]), and [tex]\( x^0 \)[/tex] (for [tex]\(4b\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x^4 + b^3x^2 + \frac{2}{3}bx + 4b
\][/tex]
4. For polynomial 25:
[tex]\(a + x\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^1 \)[/tex] (for [tex]\(x\)[/tex]) and [tex]\( x^0 \)[/tex] (for [tex]\(a\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x + a
\][/tex]
I hope this helps! Feel free to ask if you have any more questions.
1. For polynomial 22:
[tex]\(-6x + x^4 + 2x^3 - 10\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^4 \)[/tex], [tex]\( x^3 \)[/tex], [tex]\( x^1 \)[/tex] (for [tex]\(-6x\)[/tex]), and [tex]\( x^0 \)[/tex] (for [tex]\(-10\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x^4 + 2x^3 - 6x - 10
\][/tex]
2. For polynomial 23:
[tex]\(0.2mx^4 - 1.3x^5 + 0.4m^2 + 2.1x^3\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^5 \)[/tex], [tex]\( x^4 \)[/tex], [tex]\( x^3 \)[/tex], and [tex]\( x^0 \)[/tex] (for [tex]\(0.4m^2\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
-1.3x^5 + 0.2mx^4 + 2.1x^3 + 0.4m^2
\][/tex]
3. For polynomial 24:
[tex]\(4b + \frac{2}{3}bx + b^3x^2 + x^4\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^4 \)[/tex], [tex]\( x^2 \)[/tex], [tex]\( x^1 \)[/tex] (for [tex]\(\frac{2}{3}bx\)[/tex]), and [tex]\( x^0 \)[/tex] (for [tex]\(4b\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x^4 + b^3x^2 + \frac{2}{3}bx + 4b
\][/tex]
4. For polynomial 25:
[tex]\(a + x\)[/tex]
- The powers of [tex]\( x \)[/tex] in the terms are: [tex]\( x^1 \)[/tex] (for [tex]\(x\)[/tex]) and [tex]\( x^0 \)[/tex] (for [tex]\(a\)[/tex]).
- Arranging them in descending order, we get:
[tex]\[
x + a
\][/tex]
I hope this helps! Feel free to ask if you have any more questions.
