a) 3x4y2-6x3y3+x2y4
b) x2-13x+36
c) 3x2-15x
d) 4x2+4x-3
e) x2-10x+21
f) 8x2+30x+7
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Ta có: A= (3x^4 + 3x^2 + x^3 + x -3x^2 - 3) + 5x + 3
= [3x^2(x^2 + 1) + x(x^2 + 1) -3(x^2 + 1)] + 5x +3
= (x^2 + 1)(3x^2 + x - 3) + 5x +3
= B.(3x^2 + x - 3) + 5x +3
Vậy R = 5x + 3

(2y-5)(4y^2+10y+25)=2y3-125
(2-y)^3=-y^3+6y^2-12y+8
(3y+4)(9y^2-12y+16)=27y^3+64
(x-3)^3+(2-x)^3= -3x^2+15x-19
(x+y)^3-(x-y)^3= 2y^3+6x^2y

\(\frac{x^4+6x^3+9x^2-1}{x^4+6x^3+7x^2-6x+1}=\frac{x^2\left(x+3\right)^2-1}{x^4+6x^3+9x^2-2x^2-6x+1}=\)
\(=\frac{\left(x^2+3x-1\right)\left(x^2+3x+1\right)}{x^2\left(x+3\right)^2-2x\left(x+3\right)+1}=\frac{\left(x^2+3x-1\right)\left(x^2+3x+1\right)}{\left(x^2+3x-1\right)^2}\)
\(=\frac{x^2+3x+1}{x^2+3x-1}\)


Ta có :
\(\left(ax+b\right)\left(x^2-2cx+abc\right)=x^3-4x^2+3x+\frac{9}{5}\)
\(\Leftrightarrow ax^3+2acx^2+bx^2-2bcx+ab^2c=x^3-4x^2+3x+\frac{9}{5}\)
\(\Leftrightarrow ax^3+\left(2ac+b^2\right)x^2+\left(a^2bc-2bc\right)x+ab^2c=x^3-4x^2+3x+\frac{9}{5}\)
Đồng nhất hệ số ta được :
a = 1
2ac + b2 = -4
a2bc - 2bc = 3
\(ab^2c=\frac{9}{5}\)
\(\Rightarrow a=1;b=\frac{3}{5};c=5\)

a) \(3x^4y^2-6x^3y^3+x^2y^4=x^2y^2\left(3x^2-6xy+y^2\right)\)
b) \(x^2-13x+36=x^2-4x-9x+36=x\left(x-4\right)-9\left(x-4\right)=\left(x-9\right)\left(x-4\right)\)
d) \(4x^2+4x-3=4x^2-2x+6x-3=2x\left(2x-1\right)+3\left(2x-1\right)=\left(2x+3\right)\left(2x-1\right)\)
c) \(3x^2-15x=3x\left(x-5\right)\)
e) \(x^2-10x+21=x^2-3x-7x+21=x\left(x-3\right)-7\left(x-3\right)=\left(x-3\right)\left(x-7\right)\).
f) \(8x^2+30x+7=8x^2+2x+28x+7=2x\left(4x+1\right)+7\left(4x+1\right)=\left(2x+7\right)\left(4x+1\right)\)