Question

Any Genius here
1x2x4+4x2x8+3x6x12 + ... +10x20x40 = (a) 88020 (b) 44070 (c)24200. (d) 55150​

Answer 1

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.