What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

The quotient of this division is . The remainder here would be .

Step-by-step explanation:

The numerator is a polynomial about with degree .

The divisor is a polynomial, also about , but with degree .

By the division algorithm, the quotient should be of degree , while the remainder shall be of degree (i.e., the remainder would be a constant.) Let the quotient be with coefficients , , and .

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Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is . On the right-hand side, that would be . Hence .

Now, given that , rewrite the right-hand side:

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Hence:

Subtract from both sides of the equation:

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The term with a degree of two on the left-hand side has coefficient . Since the only term on the right hand side with degree two would have coefficient , .

Again, rewrite the right-hand side:

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Subtract from both sides of the equation:

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By the same logic, .

Hence the quotient would be .

step-by-step explanation: