Given Polynomial is x^4 +15x^3 +6x^2 - 12x +3
Divisor = x+2
We know that
Remainder Theorem:
Let P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial,If P(x) is divided by (x-a) then remainder is P(a).
So, P(x) is divided by (x+2) then the remainder is P(-2).
P(-2) =
⇛(-2)^4+15(-2)^3+6(-2)^2-12(-6)+3
⇛ 16+15(-8)+6(4)+72+3
⇛16-120+24+72+3
⇛ 67-120
⇛ -53
P(-2) = -53
Answer:- The remainder is -53.
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