The remainder from the division of the polynomial x^3 +ax^2 +2ax+5byx+1 is 3. Find a.

nar6jetaime86

nar6jetaime86

Answered question

2022-09-04

The remainder from the division of the polynomial x 3 + a x 2 + 2 a x + 5 b y x + 1 is 3. Find a.

Answer & Explanation

acilschoincg8

acilschoincg8

Beginner2022-09-05Added 12 answers

REMAINDER THEOREM : When a polynomial p(x) is divided by x-a, the remainder obtained is equal to p(a)
Therefore by remainder theorem, when p ( x ) = x 3 + a x 2 + 2 a x + 5 is divided by x+1, we get the remainder p(-1)
But it is given that the remainder is 3.
Therefore, we have p(-1)=3
( 1 ) 3 + a ( 1 ) 2 + 2 a ( 1 ) + 5 = 3
-1+a-2a+5=3
-a+4=3
-a=-1
a=1
Result:
a=1

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