Question

if ax^3+bx^2+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2),find the values of a and b​

Answer 1

since, x+2 is a factor of

f(x) = ax^3 + bx^2 + x - 6

f(-2) should be zero

a*(-2)^3 + b*(-2)^2 + (-2) - 6 = 0

-8a + 4b -2 - 6 = 0

-8a + 4b = 8................(1)

again,

when divided by x-2, remainder is 4

so f(2) = 4

a*2^3 + b*2^2 + 2 - 6 = 4

8a + 4b = 8

-8a + 4b = 8

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8b = 16

b = 2

a= 0