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Answer 1

Answer:

a = - 2 and b = 6

Step-by-step explanation:

Expression

${x}^{3} - 2 {x}^{2} + ax - b$

When divided by

${x}^{2} - 2x - 3$

Remainder

$x - 6$

To find a and b

Lets divide the original expression to find quotient

$\frac{{x}^{3} - 2 {x}^{2} + ax - b}{ {x}^{2} - 2x - 3 }$

Quotient is x

And the remainder is ax+3x-b

Now, we know that remainder is x-6

Hence, b = 6

and, a+3 = 1

a= 1-3 = - 2