The expression ax - 8x² + bx + 6 is exactly divisible by
x^2 - 2x - 3. Calculate the value of a and of b.

a = 3;  b = -5

Step-by-step explanation:

x² -2x-3=(x-3)(x+1)

As  it divides p(x); P(3) = 0 and P(-1) =0

P(x)= ax³ - 8x² + bx + 6

P(3) = 3³a - 8*9 + 3b + 6 =0

27a - 72 + 3b + 6 = 0

27a + 3b -66 =0

27a + 3b = 66 (i)

P(-1) = -a -8*(-1)² + b* (-1) + 6 = 0

-a - 8 -b + 6 = 0

-a - b -2 = 0

-a -b = 2    (ii)

(i)    27a + 3b = 66

(ii)*3          -3a  -3b = 6

Add            24a      = 72

                       a = 72/24

                       a = 3

Substitute a value in (ii)

-3 - b= 2

 -b = 2+3

-b= 5

b = -5

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step-by-step explanation:

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