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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 :

GinnyAnswer
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]
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