Question

the polynomial p(x) =x^4-2x^3+3x^2-ax+3a-7 when divided by (x+1),leaves the remainder 29.find the value of a ​

Answer 1

Given:

• Polynomial p(x)=x⁴-2x³+3x²-ax+3a-7 which gives remainder 19 when divided by x+1 .

To Find:

• Value of 'a'.

• 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.