Question

-The polynomial p(x) = x^4 - ax^3 – x^2 - ax + 4 when divided by X-2 leaves the remainder 4. Find the
value of x.​

Answer 1

Step-by-step explanation:

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)

               =p(−2)    (By Remainder Theorem)

               =−24−