Question

the polynomial ax cube + 3 x square - 3 and 2 x cube minus 5 x + a when divided by x minus 4 leave the same remainder find the value of a .​

Answer 1

Answer:

a=1

Step-by-step explanation:

let, P1(x) = ax³+3x²-3

P2(x) = 2x³-5x+a

To find remainders, putting x = 4 in both polynomials ( let x-4=0 => x=4)

=> P1(4) = a(4)³+3(4)²-3

= 64a + 48-3

= 64a+45

=> P2(4) = 2(4)³-5(4)+a

= 128-20+a

= a+108

since, P1(4) and P2(4) are the remainders.

according to the question,

P1(4) = P2(4)

=> 64a+45 = a+108

=> 64a - a = 108 - 45

=> 63a = 63

=> a= 1

Therefore the value of a=1

Answer 2

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