The polynomial A is represented as <u>x - 2</u>, making <u>option A</u> the right choice.
In the question, we are asked to find the correct representation of A, when the algebraic expression (x² + x)/(x + 3) can be rewritten as the algebraic expression A + 6/(x + 3), where A is a polynomial.
Thus, we can write an equation,
A + 6/(x + 3) = (x² + x)/(x + 3),
or, A + 6/(x + 3) - 6/(x + 3) = (x² + x)/(x + 3) - 6/(x + 3) {Subtracting 6/(x + 3) from the both sides of the equation}
or, A = (x² + x)/(x + 3) - 6/(x + 3) {Simplifying},
or, A = (x² + x - 6)/(x + 3) {Subtracting the two fractions with the same denominator (x + 3)},
or, A = (x² + 3x - 2x - 6)/(x + 3) {Mid-term factorization},
or, A = {x(x + 3) - 2(x + 3)}/(x + 3) {Taking common},
or, A = {(x - 2)(x + 3)}/(x + 3) {Taking (x + 3) common},
or, A = x - 2 {Cancelling (x + 3) from the numerator and the denominator}.
Thus, the polynomial A is represented as <u>x - 2</u>, making <u>option A</u> the right choice.
Learn more about polynomials at
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