Answer :

To find the quotient of the polynomial [tex]\(-35x^5 - 40x^4 + 15x^3 - 15x^2\)[/tex] divided by [tex]\(-5x^2\)[/tex], follow these steps:

1. Understand the Division: We are dividing each term of the polynomial by [tex]\(-5x^2\)[/tex].

2. Divide Each Term:

a. [tex]\(-35x^5 \div -5x^2 = 7x^{5-2} = 7x^3\)[/tex]

b. [tex]\(-40x^4 \div -5x^2 = 8x^{4-2} = 8x^2\)[/tex]

c. [tex]\(15x^3 \div -5x^2 = -3x^{3-2} = -3x\)[/tex]

d. [tex]\(-15x^2 \div -5x^2 = 3x^{2-2} = 3\)[/tex]

3. Combine the Results: Write the results from the divisions:

The quotient is [tex]\(7x^3 + 8x^2 - 3x + 3\)[/tex].

This is the simplified form of the quotient obtained by dividing the given polynomial by [tex]\(-5x^2\)[/tex].

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Rewritten by : Barada