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

Toán Lớp 8: Phân tích đa thức thành nhân tử: a) 3x² + 8x + 4 b) 4x² – 4x – 3 c) 9x² +12x – 5 d) 6x² – 11x +3 e) 2x² + 3x – 27 f) x² – 10x + 24 g)

Toán Lớp 8: Phân tích đa thức thành nhân tử:
a) 3x² + 8x + 4
b) 4x² – 4x – 3
c) 9x² +12x – 5
d) 6x² – 11x +3
e) 2x² + 3x – 27
f) x² – 10x + 24
g) 2x² – 5xy + 2y²

Comments ( 2 )

  1. Giải đáp:
    $\begin{array}{l}
    a)3{x^2} + 8x + 4\\
     = 3{x^2} + 6x + 2x + 4\\
     = \left( {x + 2} \right)\left( {3x + 2} \right)\\
    b)4{x^2} – 4x – 3\\
     = 4{x^2} – 4x + 1 – 4\\
     = {\left( {2x – 1} \right)^2} – {2^3}\\
     = \left( {2x – 1 – 2} \right)\left( {2x – 1 + 2} \right)\\
     = \left( {2x – 3} \right)\left( {2x + 1} \right)\\
    c)9{x^2} + 12x – 5\\
     = 9{x^2} + 2.3x.2 + 4 – 9\\
     = {\left( {3x + 2} \right)^2} – {3^2}\\
     = \left( {3x + 2 – 3} \right)\left( {3x + 2 + 3} \right)\\
     = \left( {3x – 1} \right)\left( {3x + 5} \right)\\
    d)6{x^2} – 11x + 3\\
     = 6{x^2} – 9x – 2x + 3\\
     = \left( {2x – 3} \right)\left( {3x – 1} \right)\\
    e)2{x^2} + 3x – 27\\
     = 2{x^2} + 9x – 6x – 27\\
     = \left( {2x + 9} \right)\left( {x – 3} \right)\\
    f){x^2} – 10x + 24\\
     = {x^2} – 4x – 6x + 24\\
     = \left( {x – 4} \right)\left( {x – 6} \right)\\
    g)2{x^2} – 5xy + 2{y^2}\\
     = 2{x^2} – xy – 4xy + 2{y^2}\\
     = \left( {2x – y} \right)\left( {x – 2y} \right)
    \end{array}$

  2. Giải đáp:
    a/ 3x^2 + 8x + 4
    = (4x^2+ 8x+4)-x^2
    =(2x+2)^2-x^2
    =(2x+2-x)(2x+2+x)
    =(x+2)(3x+2)
    b/ 4x^2-4x-3
    =(4x^2-4x+1)-4
    =(2x-1)^2-2^2
    =(2x-1-2)(2x-1+2)
    =(2x-3)(2x+1)
    c/ 9x^2+12x-5
    = (9x^2+12x+4)-9
    =(3x+2)^2-3^2
    =(3x+2-3)(3x+2+3)
    =(3x-1)(3x+5)
    d/ 6x^2-11x+3
    =(6x^2-2x)-(9x-3)
    =2x(3x-1)-3(3x-1)
    =(3x-1)(2x-3)
    e/ 2x^2+3x-27
    =(2x^2-6x)+(9x-27)
    =2x(x-3)+9(x-3)
    =(x-3)(2x+9)
    f/ x^2-10x+24
    =(x^2-10x+25)-1
    =(x-5)^2-1^2
    =(x-5-1)(x-5+1)
    =(x-6)(x-4)
    g/ 2x^2-5xy+2y^2
    = (2x^2-4xy)-(xy-2y^2)
    =2x(x-2y)-y(x-2y)
    =(x-2y)(2x-y)

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