When polynomial p(x)= x^4-2x^2+3x^2-ax+3a-7 is divided by x+1 it leaves the remainder as 19. find the value of a

Question

When polynomial p(x)= x^4-2x^2+3x^2-ax+3a-7 is divided by x+1 it leaves the remainder as 19. find the value of a

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Ariana 1 month 2021-08-15T08:53:43+00:00 5 Answers 0 views 0

Answers ( )

    0
    2021-08-15T08:54:58+00:00

    Answer:

    p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

    Divisor = x + 1

    x + 1 = 0

    x = -1

    So, substituting the value of x = – 1 in p(x),

    we get,

    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

    Since, a = 5.

    We get the polynomial,

    p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

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

    p(x) = x4 – 2×3 + 3×2 – 5x + 8

    As per the question

    ,

    When the polynomial obtained is divided by (x + 2),

    We get, x + 2 = 0

    x = – 2

    So, substituting the value of x = – 2 in p(x), we get,

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

    ⇒ p(-2) = 16 + 16 + 12 + 10 + 8

    ⇒ p(-2) = 62 Therefore, the remainder = 62.

    0
    2021-08-15T08:55:04+00:00

    Answer:

    p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

    Divisor = x + 1

    x + 1 = 0

    x = -1

    So, substituting the value of x = – 1 in p(x),

    we get,

    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

    Since, a = 5.

    We get the polynomial,

    p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

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

    p(x) = x4 – 2×3 + 3×2 – 5x + 8

    As per the question

    ,

    When the polynomial obtained is divided by (x + 2),

    We get, x + 2 = 0

    x = – 2

    So, substituting the value of x = – 2 in p(x), we get,

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

    ⇒ p(-2) = 16 + 16 + 12 + 10 + 8

    ⇒ p(-2) = 62 Therefore, the remainder = 62.

    0
    2021-08-15T08:55:09+00:00

    Answer:

    p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

    Divisor = x + 1

    x + 1 = 0

    x = -1

    So, substituting the value of x = – 1 in p(x),

    we get,

    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

    Since, a = 5.

    We get the polynomial,

    p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

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

    p(x) = x4 – 2×3 + 3×2 – 5x + 8

    As per the question

    ,

    When the polynomial obtained is divided by (x + 2),

    We get, x + 2 = 0

    x = – 2

    So, substituting the value of x = – 2 in p(x), we get,

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

    ⇒ p(-2) = 16 + 16 + 12 + 10 + 8

    ⇒ p(-2) = 62 Therefore, the remainder = 62.

    0
    2021-08-15T08:55:33+00:00

    Answer:

    x=1

    p(x)=x^4-2x^2+3x^2-ax+3a-7

    0=(1)4-2(1)+3(1)-a(1)+3a-7

    0=4-2+3-a+3a-7

    0=2a-2

    2=2a

    a=1

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    Step-by-step explanation:

    0
    2021-08-15T08:55:35+00:00

    Answer:

    p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

    Divisor = x + 1

    x + 1 = 0

    x = -1

    So, substituting the value of x = – 1 in p(x),

    we get,

    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

    Since, a = 5.

    We get the polynomial,

    p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

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

    p(x) = x4 – 2×3 + 3×2 – 5x + 8

    As per the question

    ,

    When the polynomial obtained is divided by (x + 2),

    We get, x + 2 = 0

    x = – 2

    So, substituting the value of x = – 2 in p(x), we get,

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

    ⇒ p(-2) = 16 + 16 + 12 + 10 + 8

    ⇒ p(-2) = 62 Therefore, the remainder = 62.

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