Given:
Polynomial p(x)=x⁴-2x³+3x²-ax+3a-7 which gives remainder 19 when divided by x+1
To Find:
- Value of remainder when p(x) is divided by x+2
Solution:
Dividend= x⁴-2x³+3x²-ax+3a-7
Divisor= x+1
Remainder= 19
On dividing x⁴-2x³+3x²-ax+3a-7 by x+1, we get
(Calculation in First attachment)
Remainder= 4a-1
Also, it is given that
Remainder=19
⇒ 4a-1= 19
⇒ 4a= 20
⇒ a= 5
Now, after putting value of a in dividend, we get
Dividend= x⁴-2x³+3x²-(5)x+3(5)-7
Dividend= x⁴-2x³+3x²-5x+15-7
Dividend= x⁴-2x³+3x²-5x+8
Now,
Dividend= x⁴-2x³+3x²-5x+8
Divisor= x+2
After dividing x⁴-2x³+3x²-5x+8 by x+2, we get
(Calculation in second attachment)
Remainder= 62
Hence, the value of a is 5 and required remainder is 62.Given:
