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When a certain polynomial is divided by x - 3 its quotient is xsquared - 5x - 6 and its remainder is 5 What is the polynomial?
Lauren1919
From the Division Algorithm for Polynomials theorem,
f(x) = q(x)g(x) + r(x) or we say:
dividend = (quotient)(divisor) + (remainder)
In our case,
quotient = x^2 - 5x - 6; divisor = x - 3; and remainder = 5.
Substitute what you know into the formula, and you will have:
f(x) = (x^2 - 5x - 6)(x - 3) + 5
f(x) = x^3 - 5x^2 - 6x - 3x^2 + 15x + 18 + 5
f(x) = x^3 - 5x^2 - 3x^2 - 6x + 15x + 18 + 5
f(x) = x^3 - 8x^2 + 9x + 23 (this is the required polynomial)
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