Question

6. The polynomial (px)=x^4+2x^3+3x^2-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.
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Answer 1

Answer:

Solve this problem and put remainder =19 you will get the value of a

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Answer 2

• P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.

=>x + 1 = 0

=>x = -1

Thus,

=>P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.

=>19 = 1 + 2 + 3 + a + 3a - 7

=>19 = 6 - 7 + 4a

=>4a - 1 = 19

=>4a = 20

=>a = 5

Therefore, Value of a is 5.

•P(x) = x⁴ - 2x³ + 3x² - (5)x + 3(5) - 7

=>P(x) = x⁴ - 2x³ + 3x² - 5x + 15 - 7

=>P(x) = x⁴ - 2x³ + 3x² - 5x + 8

When this polynomial is divided by (x + 2),

=>x + 2 = 0

=>x = - 2

Therefore, P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 5(-2) + 8

=>P(-2) = 16 + 16 + 12 + 10 + 8

=>P(-2) = 62

Therefore, Remainder is 62.

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