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Remainder Theorem

the polynomia...

Question

the polynomial P of x is equal to 4 x³-2 X² + px + 5 and q of x is equal to x³+ 6 X² + P leaves remainder A and B respectively when divided by X + 2 find the value of p if a + b is equal to 0

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Solution

p(x) = 4x³ -2x² + px +5
g(x) = x + 2

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Remainder Theorem : Let p(x) be an polynomial of degree greater than or equal to one. Let 'a' be any real number.If p(x) is divisible by (x-a) then the remainder is p(a)

p(-2) = 4(-2)³ - 2(-2)² + p(-2) +5
A = -32 -8 -2p +5
A = -35 -2p

f(x) = x³ + 6x² + p
q (-2) = - 8 +24 +p
B = 16+ p

A +B = 0
16 + p -35 -2p =0
p=-19

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