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

Toán Lớp 8: Phân tích các đa thức sau thành nhân tử: a) x^3 – 6x^2 – x +30; b) x^3 + 9x^2 + 23x + 15; c)x4 + 2x^3 – 16x^2 – 2x +15; d) 2x^4 – x^3 –

Tháng Một 21, 2023 Toán học 1 Comment 0 views

Toán Lớp 8: Phân tích các đa thức sau thành nhân tử:
a) x^3 – 6x^2 – x +30; b) x^3 + 9x^2 + 23x + 15;
c)x4 + 2x^3 – 16x^2 – 2x +15; d) 2x^4 – x^3 – 9x^2 +13x – 5;

Comments ( 1 )

  1. ngoclankhue
    ngoclankhue
    21 Tháng Một, 2023 at 2:35 sáng
    Reply
    a)
    x^3 – 6x^2 – x + 30
    = (x^3 – 5x^2) + (5x – x^2) + (30-6x)
    =  x^2 (x-5) – x(x-5) -6(x-5)
    = (x^2 – x – 6)(x-5)
    = (x^2 – 3x + 2x – 6)(x-5)
    = [x(x-3) + 2(x-3)] (x-5)
    = (x+2)(x-3)(x-5)
    b)
    x^3 + 9x^2 + 23x + 15
    = (x^3 + 5x^2) + (4x^2 + 20x) + (3x+15)
    = x^2 (x+5) + 4x(x+5) + 3(x+5)
    = (x^2 + 4x + 3)(x+5)
    = (x^2 + 3x + x  +3)(x+5)
    = [x(x+3) + (x+3)](x+5)
    = (x+1)(x+3)(x+5)
    c)
    x^4 + 2x^3 – 16x^2 – 2x + 15 
    = (x^4 +5x^3) + (-3x^3 -15x^2) + (-x^2 – 5x) + (3x+15)
    = x^3 (x+5) – 3x^2 (x+5) – x(x+5) + 3(x+5)
    = (x^3 – 3x^2 – x + 3)(x+5)
    = [x^2(x-3) – (x-3)] (x+5)
    = (x^2 – 1)(x-3)(x+5)
    =(x-1)(x+1)(x-3)(x+5)
    d)
    2x^4 – x^3 – 9x^2 + 13x – 5
    = (2x^4 + 5x^3) + (-6x^3 -15x^2) + (6x^2 + 15x) + (-2x-5)
    = x^3 (2x+5) – 3x^3 (2x+5) + 3x(2x+5) – (2x+5)
    = (x^3 – 3x^2 + 3x – 1)(2x+5)
    = (x-1)^3 (2x+5)
     

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

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