Q8. Write the following polynomials in standard form:

i. [tex]$4y - 4y^3 + 3 - y^4$[/tex]

ii. [tex]$5m^3 - 6m + 7 - 2m^2$[/tex]

Question

27-06-2024
Mathematics

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Q8. Write the following polynomials in standard form:

i. [tex]$4y - 4y^3 + 3 - y^4$[/tex]

ii. [tex]$5m^3 - 6m + 7 - 2m^2$[/tex]

Sagot :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-27T02:30:26-04:00

To rewrite the given polynomials in standard form, we follow these steps:

1. Identify all the terms of the polynomial.
2. Arrange the terms in descending order of the power of the variable.

Let's go through each polynomial step by step:

### Part i: $4y - 4y^3 + 3 - y^4$

1. Identify the terms: $4y$, $-4y^3$, $3$, and $-y^4$.
2. Arrange the terms in descending order of the power of $y$:
- The term with $y^4$ comes first.
- The term with $y^3$ comes next.
- The term with $y$ follows that.
- The constant term comes last.

So, the polynomial in standard form is:

[tex]\[ -y^4 - 4y^3 + 4y + 3 \][/tex]

### Part ii: $5m^3 - 6m + 7 - 2m^2$

1. Identify the terms: $5m^3$, $-6m$, $7$, and $-2m^2$.
2. Arrange the terms in descending order of the power of $m$:
- The term with $m^3$ comes first.
- The term with $m^2$ comes next.
- The term with $m$ comes after that.
- The constant term comes last.

So, the polynomial in standard form is:

[tex]\[ 5m^3 - 2m^2 - 6m + 7 \][/tex]

### Conclusion
The standard form of the given polynomials are:

i. $ -y^4 - 4y^3 + 4y + 3 $

ii. [tex]$ 5m^3 - 2m^2 - 6m + 7 $[/tex]

Sagot :

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