P(x)=x^4 - 2x^3 - 3x^2 + 4
What is the remainder when P(x) is divided by (x-3)?

The given polynomial is p(x)=x  

4

−2x  

3

+3x  

2

−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)=x  

4

−2x  

3

+3x  

2

−5x+3×5−7

       =x  

4

−2x  

3

+3x  

2

−5x+15−7

       =x  

4

−2x  

3

+3x  

2

−5x+8

Remainder when the polynomial is divided by (x+2)

              =p(−2)    (By Remainder Theorem)

              =−2  

4

−2(−2)  

3

+3(−2)  

2

−5(−2)+8

              =16+16+12+10+8

              =62

Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62

Step-by-step explanation:

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