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SOLVE for when the expression 4x²-3x-8 divided by x-a, and reminder is 2, what is the value a?( With solution)



Sagot :

let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem,

f(a) = 4a^2 - 3a - 8 = 2

4a^2 - 3a - 10 = 0

(a-2)(4a + 5) = 0

a = 2 or a = -5/4

the 2nd is done the same way:

f(3) = 81 + 9m + 3n + 5 = 128

9m + 3n = 42

3m + n = 14

f(-1) = -3 - m - n + 5 = 4

-m-n = 2

add them:

2m = 16

m = 8 , then 24 + n = 14 ----> n = -10

so f(x) = 3x^3 + 8x^2 -10x + 5

f(3) = 81 + 72 - 30 + 5 = 12