Answer :
To rearrange the polynomial [tex]\(10 - 7x^3 + 8x\)[/tex] in standard form, we need to order the terms according to the powers of [tex]\(x\)[/tex] in descending order.
1. Identify the terms and their powers:
- [tex]\(10\)[/tex] (constant term, [tex]\(x^0\)[/tex])
- [tex]\(-7x^3\)[/tex] (term with [tex]\(x^3\)[/tex])
- [tex]\(8x\)[/tex] (term with [tex]\(x\)[/tex])
2. Arrange these terms so that the powers of [tex]\(x\)[/tex] decrease from left to right.
Let's explicitly write out the rearrangement process:
- The term with the highest power is [tex]\(-7x^3\)[/tex].
- The next term is [tex]\(8x\)[/tex], which has a power of [tex]\(x^1\)[/tex].
- The constant term, which has no [tex]\(x\)[/tex], is [tex]\(10\)[/tex].
Thus, when we rearrange [tex]\(10 - 7x^3 + 8x\)[/tex] in decreasing order of the powers of [tex]\(x\)[/tex], we get:
[tex]\[ -7x^3 + 8x + 10 \][/tex]
Now, we compare this rearranged form to the given options:
a) [tex]\(-7x^3 + 5x + 15\)[/tex]
b) [tex]\(10 - 7x^3 + 8x\)[/tex]
c) [tex]\(8x + 10 - 7x^3\)[/tex]
d) [tex]\(-7x^3 + 8x + 10\)[/tex]
The correct answer is clearly:
d) [tex]\(-7x^3 + 8x + 10\)[/tex]
So, the polynomial [tex]\(10 - 7x^3 + 8x\)[/tex] rearranged in standard form is [tex]\( -7x^3 + 8x + 10 \)[/tex], and the correct choice is (d).
1. Identify the terms and their powers:
- [tex]\(10\)[/tex] (constant term, [tex]\(x^0\)[/tex])
- [tex]\(-7x^3\)[/tex] (term with [tex]\(x^3\)[/tex])
- [tex]\(8x\)[/tex] (term with [tex]\(x\)[/tex])
2. Arrange these terms so that the powers of [tex]\(x\)[/tex] decrease from left to right.
Let's explicitly write out the rearrangement process:
- The term with the highest power is [tex]\(-7x^3\)[/tex].
- The next term is [tex]\(8x\)[/tex], which has a power of [tex]\(x^1\)[/tex].
- The constant term, which has no [tex]\(x\)[/tex], is [tex]\(10\)[/tex].
Thus, when we rearrange [tex]\(10 - 7x^3 + 8x\)[/tex] in decreasing order of the powers of [tex]\(x\)[/tex], we get:
[tex]\[ -7x^3 + 8x + 10 \][/tex]
Now, we compare this rearranged form to the given options:
a) [tex]\(-7x^3 + 5x + 15\)[/tex]
b) [tex]\(10 - 7x^3 + 8x\)[/tex]
c) [tex]\(8x + 10 - 7x^3\)[/tex]
d) [tex]\(-7x^3 + 8x + 10\)[/tex]
The correct answer is clearly:
d) [tex]\(-7x^3 + 8x + 10\)[/tex]
So, the polynomial [tex]\(10 - 7x^3 + 8x\)[/tex] rearranged in standard form is [tex]\( -7x^3 + 8x + 10 \)[/tex], and the correct choice is (d).
