Question

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

Answer 1

The quotient $x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5$ is $x^3 + 2x - 3$

How to determine the quotient?

The quotient can be represented as:

$x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5$

Start by expanding the dividend

$x^5 + 2x^3 - 5x^3 - 3x^2 - 10x + 15 \div x^2 - 5$

Rewrite as:

$x^5 + 2x^3 - 3x^2 - 5x^3 - 10x + 15 \div x^2 - 5$

Factorize the dividend

$x^2(x^3 + 2x - 3) - 5(x^3 + 2x - 3) \div x^2 - 5$

Factor out x^3 + 2x - 3

$(x^2- 5)(x^3 + 2x - 3) \div x^2 - 5$

Cancel out the common factor

$x^3 + 2x - 3$

Hence, the quotient $x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5$ is $x^3 + 2x - 3$

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