## The polynomial p (x)= x⁴-2x³+3x²-ax+3a-7 when divided by (x+1) leaves the remiander 19. Find the value of A and also divide it by (x+2)

Question

The polynomial p (x)= x⁴-2x³+3x²-ax+3a-7 when divided by (x+1) leaves the remiander 19. Find the value of A and also divide it by (x+2)

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5 days 2021-11-24T20:57:34+00:00 2 Answers 0 views 0

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.