Phân tích bằng hai cách a ) 7x – 6x^2 – 2 b ) 16x – 5x^2 – 3 c ) x^2 – 9x + 20 d ) 2x^2 – 5x -12 Phân tích bằng 1 cách a) x^4 + 4 b ) x^4 + x^2 + 1 c

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1. Đáp án:

    

   Giải thích các bước giải:

   $a,7x-6x^2-2$

   $=-(6x^2-7x+2)$

   $=-(6x^2-3x-4x+2)$

   $=-(3x-2)(2x-1)$

   $b,16-5x^2-3$

   $=-(5x^2-16x+3)$

   $=-(5x-1)(x-3)$

   $c,x^2-9x+20$

   $=x^2-4x-5x+20$

   $=(x-4)(x-5)$

   $d,2x^2-5x-12$

   $=2x^2-8x+3x-12$

   $=(2x+3)(x-4)$

   $a,a^4+4=a^4+4a^2+4-4a^2$

   $=(a^2+2)^2-(2a)^2$

   $=(a^2+2-2a)(a^2+2+2a)$

   $b,x^4+x^2+1$

   $=x^4+2x^2+1-x^2$

   $=(x^2+1)^2-x^2$

   $=(x^2-x+1)(x^2+x+1)$

   $d,x^5+x+1$

   $=x^5-x^2+x^2+x+1$

   $=x^2(x^3-1)+(x^2+x+1)$

   $=x^2(x-1)(x^2+x+1)+(x^2+x+1)$

   $=(x^3-x^2+x^2+x+1)(x-1)$

   $=(x^3+x+1)(x-1)$

   $d,x^4+4y^2$

   $=x^4+4x^2y^2-4x^2y^2$

   $=(x^2+2y^2)-(2xy)^2$

   $=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$

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2. a)-6x²+7x-2=-6x²+4x+3x-2=-2x(3x-2)+(3x-2)=(-2x+1)(3x-2)

   b)-5x²+16x-3=-5x²+15x+x-3=-5x(x-3)+(x-3)=(-5x+1)(x-3)

   c)x²-4x-5x+20=x(x-4)-5(x-4)=(x-4)(x-5)

   d)2x²-8x+3x-12=2x(x-4)+3(x-4)=(2x+3)(x-4)

   a)x^4+4=x^4-4x²+4x²+4=(x^4+4x²+4)-4x²=(x²+2)²-4x²=(x²+2-4x)(x²+2+4x)

   b)x^4+x^2+1=x^4+x^2+1+x-x=x(x³-1)+x²+x+1=x(x-1)(x²+x+1)+(x²+x+1)

      =(x²+x+1)[x(x-1)+1]=(x²+x+1)(x²-x+1)

   c)x^5+x+1=x^5-x²+x²+x+1=x²(x³-1)+x²+x²+x+1=x²(x-1)(x²+x²+x+1)+x²+x²+x+1

     =(x²+x²+x+1)(x³-x²+1)

   d)x^4+4y^4=(x²)²+4x²y²+(2y²)²-4x²y²=(x²+2y²)²-(2xy)²=(x²+2y²-2xy)(x²+2y²+2xy)

    

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