On a true/false exam, the ratio of true questions is 6 to 7. one student replies the exam only has 13 questions explain the possible flaw in the students reasoning

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Ответ:

AshNic

11.07.2022

Mathematics

solution:

we have been asked to find the quotient of (x^3 – 3x^2 + 5x – 3) ÷ (x – 1)

it can be re-written as follows:

$\frac{(x^3-3x^2+5x-3)}{(x-1)}= \frac{x^3-x^2-2x^2+2x+3x-3}{(x-1)}\\ \\\frac{(x^3-3x^2+5x-3)}{(x-1)}= \frac{x^2(x-1)-2x(x-1)+3(x-1)}{(x-1)}\\\\\frac{(x^3-3x^2+5x-3)}{(x-1)}= \frac{(x-1)(x^2-2x+3)}{(x-1)}\\\\\text{cancel out the like terms from numerator and denominator we get}\\\\\frac{(x^3-3x^2+5x-3)}{(x-1)}=(x^2-2x+3)$

hence the correct option is x^2 – 2x + 3

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