What is the value of a and b if x^2-4 is a factor of ax^4 +2x^3 - 3x^2 +bx-4
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A = 1
B = -8
Factorize X^2-4 = (X+2) (X-2)
use Factor Theorem
if X^2 - 4 is a factor of ax^4 +2x^3 - 3x^2 +bx-4 (let's say P(x) )
then the Remainder will be 0 when dividing P(X) by x^2-4
Find Zero of X^2 - 4
(X-2)(x+2 ) = 0
X= +2
X = -2
Using Factor Theorem
then P(2) = 0
& P(-2) = 0
as x^2-4 is factor of P(x)
P(2) = 8a-b = 0
p(-2) = 16a -2b -32 =0
simplify both equations to get values of A and B
B = -8
Factorize X^2-4 = (X+2) (X-2)
use Factor Theorem
if X^2 - 4 is a factor of ax^4 +2x^3 - 3x^2 +bx-4 (let's say P(x) )
then the Remainder will be 0 when dividing P(X) by x^2-4
Find Zero of X^2 - 4
(X-2)(x+2 ) = 0
X= +2
X = -2
Using Factor Theorem
then P(2) = 0
& P(-2) = 0
as x^2-4 is factor of P(x)
P(2) = 8a-b = 0
p(-2) = 16a -2b -32 =0
simplify both equations to get values of A and B
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