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The quotient of (x5 – 3x3 – 3x2 – 10x + 15) and (x2 – 5) is a polynomial. What is the quotient?

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MrRoyalidn

The quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]

How to determine the quotient?

The quotient can be represented as:

[tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]

Start by expanding the dividend

[tex]x^5 + 2x^3 - 5x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]

Rewrite as:

[tex]x^5 + 2x^3 - 3x^2 - 5x^3 - 10x + 15 \div x^2 - 5[/tex]

Factorize the dividend

[tex]x^2(x^3 + 2x - 3) - 5(x^3 + 2x - 3) \div x^2 - 5[/tex]

Factor out x^3 + 2x - 3

[tex](x^2- 5)(x^3 + 2x - 3) \div x^2 - 5[/tex]

Cancel out the common factor

[tex]x^3 + 2x - 3[/tex]

Hence, the quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]

Read more about polynomials at:

https://brainly.com/question/1498111

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