Question

Evaluate The quantity of x cubed plus 3x squared minus 2x plus 7 divided by the quantity of x minus 2 end quantity period.

Answer 1

The value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)

What is a quotient?

Quotients involve the result of dividing a dividend by a divisor.

In other words, quotient means division or the result of a division operation

How to solve the quotient?

The quotient expression is given as:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2)

Hence, the value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)

Read more about quotients at:

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Complete question

Evaluate (x^3 + 3x^2 - 2x + 7)/x- 2