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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Tìm đa thức M a) x^3-5x^2+x-5=(x-5).M b) (x^4-x^3-4x^2-5x-3):M=x^2+x+1

Tháng Bảy 29, 2022 Toán học 2 Comments 0 views

Toán Lớp 8: Tìm đa thức M
a) x^3-5x^2+x-5=(x-5).M
b) (x^4-x^3-4x^2-5x-3):M=x^2+x+1

Comments ( 2 )

  1. tonhu12
    tonhu12
    29 Tháng Bảy, 2022 at 2:18 chiều
    Reply
    $\text{a) x³ – 5x² + x – 5 = (x – 5)M}$
    $\text{⇔ M = $\dfrac{x³ – 5x² + x – 5}{x – 5}$ $=$ $\dfrac{x^2 (x – 5) + (x – 5)}{x – 5}$ $=$ $\dfrac{(x – 5)(x^2 + 1)}{x – 5}$ $=$ $x^2 + 1$}$
    $\text{KL: Vậy M = $x^2 + 1$}$
    $\text{b) ($x^4$ – x³ – 4x² – 5x – 3) : M = x² + x + 1}$
    $\text{⇔ $x^4$ – x³ – 4x² – 5x – 3 = (x² + x + 1).M}$
    $\text{⇔ $x^4$ + x³ + x² – 2x³ – 2x² – 2x – 3x – 3x² – 3 = M(x² + x + 1)}$
    $\text{⇔ x²(x² + x + 1) – 2x(x² + x + 1) – 3(x² + x + 1) = M(x² + x + 1)}$
    $\text{⇔ (x² + x + 1)(x² – 2x – 3 = M(x² + x + 1)}$ $\\$
    $\text{⇔ M = $\dfrac{(x² + x + 1)(x² – 2x – 3)}{x² + x + 1}$ $=$ $x^2 – 2x – 3$ }$ $\\$ $\text{KL: M = $x^2 $ – 2x – 3}$
    @tryphena

  2. thanhtung
    thanhtung
    29 Tháng Bảy, 2022 at 2:17 chiều
    Reply
    #tnvt
    a)x^3-5x^2+x-5=(x-5).M
    <=>x^2(x-5)+(x-5)=M.(x-5)
    <=>(x-5)(x^2+1)=M.(x-5)
    ->M=x^2+1
    $\\$
    b)(x^4-x^3-4x^2-5x-3):M=x^2+x+1
    <=>x^4-x^3-4x^2-5x-3=M.(x^2+x+1)
    <=>x^4+x^3+x^2-2x^3-2x^2-2x-3x^2-3x-3=M.(x^2+x+1)
    <=>x^2(x^2+x+1)-2x(x^2+x+1)-3(x^2+x+1)=M.(x^2+x+1)
    <=>(x^2+x+1)(x^2-2x-3)=M.(x^2+x+1)
    =>M=x^2-2x-3
    $\\$

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222-9+11+12:2*14+14 = ? ( )

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