the polynomial p(x)=x^4-2x^3+3x^2-ax+3a-7 when divided by x+1 leaves the remainder 20, find value of a . also find remainder when p(x) is divided by x+2
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a=5;62
The given polynomial is p(x)=x4−2x3+3x2−ax+3a−7
Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19
Therefore, p(−1)=19 (By Remainder theorem)
=>(−1)4−2×(−1)3+3(−1)2−(−1)a+3a−7=19
=>1+2+3+a+3a−7=19
=>4a−1=19
=>4a=20
=>a=5
The value of a is 5
Now,
p(x)=x4−2x3+3x2−5x+3×5−7
=x4−2x3+3x2−5x+15−7
=x4−2x3+3x2−5x+8
Remainder when the polynomial is divided by (x+2)
=
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