Math, asked by deebasrib61, 8 months ago

The polynomial p(x) = 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.

Answers

Answered by ronaldoChristiano

The given polynomial is p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7.

$\color{green}{Given}$ , the polynomial p(x) when divided by (x + 1) leaves remainder 19.

∴ p(– 1) = 19 (Remainder Theorem)

⇒ (–1)4 –2(– 1)3 + 3 (–1)2 – a(–1) + 3a – 7 = 19

⇒ 1 + 2 + 3 + a + 3a – 7 = 19

⇒ 4a – 1 = 19

⇒ 4a = 19 + 1 = 20

⇒ a = 5

∴The value of a is 5.

When a = 5, we have

p(x) = x4 – 2x3 + 3x2 – 5x + 3 × 5 – 7 = x4 – 2x3 + 3x2 – 5x + 15 – 7 = x4 – 2x3 + 3x2 – 5x + 8

Remainder when the polynomial is divided by (x + 2)

= p(– 2)

= (– 2)4 – 2( – 2)3 + 3(– 2)2 – 5(– 2) + 8

= 16 + 16 + 12 + 10 + 8

= 62

Thus, the remainder when the polynomial is divided by (x + 2) is 62.

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Answered by brainly318

Answer:

The polynomial p(x) = 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.

Step-by-step explanation:

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