Question

When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.

Answer 1

ANSWER :–

A = 4 and B = -5

EXPLANATION :–

GIVEN :–

• A Polynomial P(x) = x⁵ + 2x³ + Ax + B, where A and B are constants.

• When polynomial divided by x - 1 , the remainder is 2 .

• When polynomial divided by x + 3 , the remainder is -314

TO FIND :–

Values of A and B .

SOLUTION :–

• If polynomial is divided by x - 1 then x = 1 will satisfy the equation –

=> p(1) = 2

=> (1)⁵ + 2(1)³ + A(1) + B = 2

=> 1 + 2 + A + B = 2

=> A + B = -1 ————————eq.(1)

• Now p(x) is divided by x + 3 then –

=> p(-3) = -314

=> (-3)⁵ + 2(-3)³ + A(-3) + B = -314

=> -243 - 54 - 3A + B = -314

=> -297 - 3A + B = -314

=> -3A + B = -314 + 297

=> -3A + B = -17 ––——–————eq.(2)

• Now subtract eq.(1) by eq.(2) –

=> A + B - ( -3A + B ) = - 1 - (- 17)

=> 4A = 16

=> A = 4

• Put the value of 'A' in eq.(1) –

=> 4 + B = -1

=> B = -5

Answer 2

dear Ak has done...

n Ak thank u