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\(x^3+6x+7=x^2\left(x+1\right)-x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x^2-x+7\right)\)
A = x^3 + 6x + 7
A = x^3 - x + 7x + 7
A = x(x^2 - 1) + 7(x + 1)
A = x(x - 1)(x + 1) + 7(x + 1)
A = (x + 1)[x(x - 1) + 7)
c, \(2x^2+x-3=x\left(2x-3\right)\)
d, \(6x^2-x-15=x\left(6x-15\right)\)
TK MIK NHA
\(2x^2+x-3=2x^2-2x+3x-3=2x\left(x-1\right)+3\left(x-1\right)=\left(x-1\right)\left(2x+3\right) \)
a) nhận xét hệ số : 1 + 4 - 29 + 24 = 0
=> x3 + 4x2 - 29x + 24 = x2(x-1) + 5x(x-1) - 24(x-1)
= (x-1)(x2+5x-24) = (x-1)(x-3)(x+8)
b) ...
a) \(x^3+4x^2-29x+24\)=\(\left(x+8\right)\left(x^2-4x+3\right)\)=\(\left(x+8\right)\left(x^2-x-3x+3\right)\)=\(\left(x+8\right)\left(x-1\right)\left(x-3\right)\)
b) \(x^4+6x^3+7x^2-6x+1\)=\(x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)=\(x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)^2\)
- 3x2 + (x2 - 6x + 9)
= (x - 3)2 - 3x2 = (x - 3 - \(\sqrt{3}x\))(x - 3 + \(\sqrt{3}x\))
x3 - 6x2 - x + 30
= (x + 2).x2 - 6x2 - x + 30/x + 2
= x2 - 8x + 15
= (x + 2)(x - 3)(x - 5)
\(x^3-6x^2-x+30\)
\(=\left(x^3-8x^2+15x\right)+\left(2x^2-16x+30\right)\)
\(=x\left(x^2-8x+15\right)+2\left(x^2-9x+15\right)\)
\(=\left(x^2-8x+15\right)\left(x+2\right)\)
\(=\left(x^2-3x-5x+15\right)\left(x+2\right)\)
\(=\left[x\left(x-3\right)-5\left(x-3\right)\right]\left(x+2\right)\)
\(=\left(x-5\right)\left(x-3\right)\left(x+2\right)\)
Đề có đúng không bạn
`x^2-6x+7=(x^2-6x+9)-2=(x-3)^2-(sqrt2)^2=(x-3-sqrt2)(x-3+sqrt2)`