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Ta có:
\(\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x-6\right)+32x^2\)
\(=\left(x^2-7x+6\right)\left(x^2+5x+6\right)+32x^2\)
Đặt : \(x^2+6=a\left(a< 0\right)\). Khi đó pt trở thành:
\(\left(a-7x\right)\left(a+5x\right)+32x^2\)
\(=a^2-2ax-3x^2=\left(a+x\right)\left(a-3x\right)\)
\(=\left(x^2+x+6\right)\left(x^2-3x+6\right)\)
Ta có \(x^4+10x^3+32x^2+40x+16=\left(x^4+2x^3\right)+\left(8x^3+16x^2\right)+\left(16x^2+32x\right)+\left(8x+16\right)\)
\(=x^3\left(x+2\right)+8x^2\left(x+2\right)+16x\left(x+2\right)+8\left(x+2\right)\)
\(=\left(x+2\right)\left(x^3+8x^2+16x+8\right)=\left(x+2\right)\left(x+2\right)\left(x^2+6x+4\right)\)
\(=\left(x+2\right)^2\left(x^2+6x+4\right)\)
a) \(-10x^2-17x+6\)
\(=-10x^2-20x+3x+6\)
\(=-10x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(3-10x\right)\)
b)\(x^2-10x+9\)
\(=x^2-x-9x+9\)
\(=x\left(x-1\right)-9\left(x-1\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
c) \(x^2-10x+24\)
\(=x^2-4x-6x+24\)
\(=x\left(x-4\right)-6\left(x-4\right)\)
\(=\left(x-4\right)\left(x-6\right)\)
(x - 4)(x2 + 4x + 16) - x(x2 - 6) = 2
x3 - 64 - x3 + 6x = 2
6x = 2 + 64
6x = 66
x = 66 : 6
x = 11
x3 - 27 + 3x(x - 3)
= (x - 3)(x2 + 3x + 9) + 3x(x - 3)
= (x - 3)(x2 + 3x + 9 + 3x)
= (x - 3)(x2 + 6x + 9)
= (x - 3)(x + 3)2
5x3 - 7x2 + 10x - 14
= 5x(x2 + 2) - 7(x2 + 2)
= (x2 + 2)(5x - 7)
\(x^2+x-6=\left(x^2-3x\right)+\left(2x-6\right)=x\left(x-3\right)+2\left(x-3\right)=\left(x-3\right)\left(x+2\right)\)
\(\left(x^2+x\right)^2+3\left(x^2+x\right)+2=\left(x^2+x\right)^2+2.\left(x^2+x\right).1,5+1,5^2-0,5^2\)
\(=\left(x^2+x+1,5\right)^2-0,5^2\)
\(=\left(x^2+x+1\right)\left(x^2+x+2\right)\)
Đặt \(x^2+x+1=t\)
\(\Rightarrow\left(x^2+x+1\right).\left(x^2+3x+1\right)+x^2\)
\(=t.\left(t+2x\right)+x^2\)
\(=t^2+2tx+x^2\)
\(=\left(t+x\right)^2\)
\(=\left(x^2+2x+1\right)^2\)
Lời giải:
a) Sai đề
b) \((x-1)(x+2)(x+3)(x-6)+32x^2\)
\(=[(x-1)(x-6)][(x+2)(x+3)]+32x^2\)
\(=(x^2-7x+6)(x^2+5x+6)+32x^2\)
\(=a(a+12x)+32x^2\) (đặt \(x^2-7x+6=a\) )
\(=a^2+12ax+32x^2\)
\(=a^2+4ax+8ax+32x^2\)
\(=a(a+4x)+8x(a+4x)\)
\(=(a+8x)(a+4x) \)
\(=(x^2+x+6)(x^2-3x+6)\)