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Divide the following polynomial and then place the answer in the proper location on the grid.

[tex]\[ 8y^{10} \div 4y^5 \][/tex]


Sagot :

Sure, let's go through the steps to divide the polynomial [tex]\(8y^{\top}\)[/tex] by [tex]\(4y^5\)[/tex].

1. Write down the division: We are given the polynomial [tex]\(8y^{\top}\)[/tex] divided by [tex]\(4y^5\)[/tex].

[tex]\[ \frac{8y^{\top}}{4y^5} \][/tex]

2. Divide the coefficients: The coefficients are 8 and 4. Dividing these gives:

[tex]\[ \frac{8}{4} = 2 \][/tex]

3. Divide the variables with exponents: Let’s handle the [tex]\(y\)[/tex] terms now. When you divide variables with the same base, you subtract the exponents:

[tex]\[ y^{\top} \div y^5 = y^{\top - 5} \][/tex]

Since TOP in math usually means highest degree and we are not given the exact value, we'll use a variable [tex]\(n\)[/tex] to represent the exponent higher degree.

Therefore,

[tex]\[ y^{\top - 5} \rightarrow y^{n - 5} \][/tex]

4. Combine the results: Combining the coefficients and the simplified variable terms, we get:

[tex]\[ 2y^{n - 5} \][/tex]

Placing our final answer in the proper location on the grid:

[tex]\[ 2y^{n - 5} \][/tex]