cho 2 đa thức f(x)= x² + 3x³ – 9x – 7 – 5x + 2x³ +3x²+ x – 4x+3 g(x)= 2 + 2x³ -7x – 2x + x³ + 5x² – 5x + -x -3x² – x a) tính f(x) +g(x) ; f(x)-g(x) ;

0 bình luận về “cho 2 đa thức f(x)= x² + 3x³ – 9x – 7 – 5x + 2x³ +3x²+ x – 4x+3 g(x)= 2 + 2x³ -7x – 2x + x³ + 5x² – 5x + -x -3x² – x a) tính f(x) +g(x) ; f(x)-g(x) ;”

1. a) Rút gọn: $+) f(x)= x² + 3x³ – 9x – 7 – 5x + 2x³ +3x²+ x – 4x+3$

   $f(x) = (x² + 3x²) + (3x³ + 2x³) + (-9x – 4x -5x + x) + (3-7)$

   $f(x) = 5x³ + 4x² – 17x – 4$

   .

   +) $g(x)= 2 + 2x³ -7x – 2x + x³ + 5x² – 5x  -x -3x² – x$

   $g(x)= (2x³+ x³) -(7x + 2x)  + (5x ²- 3x²) – (5x  + x  + x) + 2$

   $g(x)= 3x³ + 2x² – 16x + 2$

   .

   +) $f(x) +g(x) = (5x³ + 4x² – 17x – 4) + (3x³ + 2x² – 16x + 2)$

   $= 5x³ + 4x² – 17x – 4 + 3x³ + 2x² – 16x + 2$

   $= (5x³ + 3x³) + (4x²+ 2x²) + (-17x – 16 x) + (2 – 4)$

   $= 8x³ + 6x² – 33x – 2$

   .

   +) $f(x) – g(x) = (5x³ + 4x² – 17x – 4) – (3x³ + 2x² – 16x + 2)$

   $= 5x³ + 4x² – 17x – 4 – 3x³ – 2x² + 16x – 2$

   $= (5x³ – 3x³) + ( 4x²- 2x²) + (- 17x+ 16x) + ( -4 – 2)$

   $= 2x³ + 2x² – x – 6$

   .

   +) $g(x) –  f(x) = (3x³ + 2x² – 16x + 2) – (5x³ + 4x² – 17x – 4)$

   $= 3x³ + 2x² – 16x + 2 – 5x³ – 4x² + 17x + 4$

   $= ( 3x³ – 5x³) + (2x²- 4x²) + (-16x + 17x) + (2+4)$

   $= -2x³ – 2x² + x + 6$

   .

   Trả lời

2. a,

   $f(x)+g(x)$

   $=(x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3)+(2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x)$

   $=x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3+2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x$

   $=(x^2+3x^2+5x^2-3x^2)+(3x^3+2x^3+2x^3+x^3)+(-9x-5x+x-4x-7x-2x-5x-x-x)+(-7+3+2)$

   $=6x^2+8x^3-33x-2$

   $f(x)-g(x)$

   $=(x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3)-(2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x)$

   $=x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3-2-2x^3+7x+2x-x^3-5x^2+5x+x+3x^2+x$

   $=(x^2+3x^2-5x^2+3x^2)+(3x^3+2x^3-2x^3-x^3)+(-9x-5x+x-4x+7x+2x+5x+x+x)+(-7+3-2)$

   $=2x^2+2x^3-x-6$

   $g(x)-f(x)$

   $=(2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x)-(x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3)$

   $=2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x-x^2-3x^3+9x+7+5x-2x^3-3x^2-x+4x-3$

   $=(2+7-3)+(2x^3+x^3-3x^3-2x^3)+(-7x-2x-5x-x-x+9x+5x-x+4x)+(5x^2-3x^2-x^2-3x^2)$

   $=6-2x^3+x-2x^2$

   b, $f(x)=x^2+3x^3-9x-7-5x+2x^3+3x^2+x-4x+3$

   $=(x^2+3x^2)+(3x^3+2x^3)+(-9x-5x+x-4x)+(-7+3)$

   $=4x^2+5x^3-17x-4$

   Thay $x=0$ vào $f(x)$ ta được:

   $f(x)=4.0^2+5.0^3-17.0-4=0+0-0-4=-4$

   $\to x=0$ không là nghiệm của $f(x)$

   $g(x)=2+2x^3-7x-2x+x^3+5x^2-5x-x-3x^2-x$

   $=2+(2x^3+x^3)+(-7x-2x-5x-x-x)+(5x^2-3x^2)$

   $=2+3x^3-16x+2x^2$

   Thay $x=0$ vào $g(x)$ ta được:

   $g(x)=2+3.0^3-16.0+2.0^2=2+0=0+0=2$

   $\to x=0$ không là nghiệm của $g(x)$

   P/S: Bạn xem lại đề.

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