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if the polynomials az³ + 4z² + 3z - 4 = 0 and z³ - 4z + a = 0 leaves the same remainder when divided by z - 3, find value of a
z - 3 = 0
z = 3
substitute z in both polynomials
both polynomials leaves same remainder so equate both equation
so,
a(3)³ + 4(3)² + 3(3) - 4 = (3)³ - 4(3) + a
27a + 36 + 9 - 4 = 27 - 12 + a
27a + 41 = 15 + a
27a - a = -41 + 15
26a = - 26
a = -1
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z - 3 = 0
z = 3
substitute z in both polynomials
both polynomials leaves same remainder so equate both equation
so,
a(3)³ + 4(3)² + 3(3) - 4 = (3)³ - 4(3) + a
27a + 36 + 9 - 4 = 27 - 12 + a
27a + 41 = 15 + a
27a - a = -41 + 15
26a = - 26
a = -1
#mark as brainliest
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