Question

The polynomial p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7 when divided by x + 1 leaves the
remainder 19. Find the value of a. Also, find the remainder when p(x) is divided by x+2.​

Answer 1

Answer:

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.

Answer 2

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