Find the remainder and quotient obtained by dividing x3 – 5x2 + 7x +

1.	Find the remainder and quotient obtained by dividing x3 – 5x2 + 7x + 3by (x + 2).
Answer» Let quotient = x² + ax + b and remainder be c, then x³ – 5x² + 7x + 3 =(x + 2)(x² + ax + b) + c + = x³ – 5x² + 7x + 3 = x³ + ax² + bx + 2x² + 2ax + 2b + c = x³ +( a + 2) x² + (b + 2a)x + 2b + c From this equation, a + 2 = –5, b + 2a = 7, 2b + c = 3 i.e., a = –7 b= 21 c = -39 quotient = x² – 7x + 21, remainder = –39

Find the remainder and quotient obtained by dividing x3 – 5x2 + 7x + 3by (x + 2).

Answer»

Let quotient = x² + ax + b and remainder be c, then

x³ – 5x² + 7x + 3 =(x + 2)(x² + ax + b) + c + = x³ – 5x² + 7x + 3 = x³ + ax² + bx + 2x² + 2ax + 2b + c

= x³ +( a + 2) x² + (b + 2a)x + 2b + c From this equation,

a + 2 = –5,

b + 2a = 7, 2b + c = 3

i.e., a = –7

b= 21

c = -39

quotient = x² – 7x + 21,

remainder = –39

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Find the remainder and quotient obtained by dividing x3 – 5x2 + 7x + 3by (x + 2).

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