Question

when a polynomial 2 x cube + 3 X square + a x + b is divided by x minus 2 leaves remainder 2 and X + 2 leaves remainder minus 2 then find a and b

Answer 1

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Answer 2

Answer:

Value of a is -7 and Value of b is -12

Step-by-step explanation:

Given polynomial:

p(x) = 2x³ + 3x² + ax + b

To find: Value of a and b

We use remainder theorem to form 2 equation in 2 variable.

Remainder Theorem states that if a polynomial oh any degree say q(x) is divided by a linear polynomial of form x - b then the remainder = q(b).

So,

when p(x) is divided by x - 2 ,

Remainder = 2

p(2) = 2

2(2)³ + 3(2)² + a(2) + b = 2

16 + 12 + 2a + b = 2

2a + b = 2 - 28

2a + b = -26 ...............................(1)

when p(x) is divided by x + 2 ,

Remainder = -2

p(-2) = -2

2(-2)³ + 3(-2)² + a(-2) + b = -2

-16 + 12 - 2a + b = -2

-2a + b = -2 + 4

-2a + b = 2 ...............................(2)

Add (1) and (2)

b + b = -26 + 2

2b = -24

b = -12

Put value of b in (1)

2a + (-12) = -26

2a = -26 + 12

2a = -14

a = -7

Therefore, Value of a is -7 and Value of b is -12