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=(x+2)(x+5)(x+3)(x+4)-24
=(x2+2x+5x+10)(x2+3x+4x+12)-24
=((x2+7x+11)-1)((x2+7x+11)+1)-24
=(x2+7x+11)2-12-24
=(x2+7x+11)2-25
=(x2+7x+11)2-52
=(x2+7x+11-5)(x2+7x+11+5)
=(x2+7x+6)(x2+7x+16)
=(x2+x+6+6x)(x2+7x+16)
=(x(x+1)+6(x+1))(x2+7x+16)
=(x+6)(x+1)(x2+7x+16)
Tick cho mình nhé
a, k ph đc
b,Đặt \(A=...=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-24=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)
Đặt x^2+5x+4=t,ta có:
\(A=t\left(t+2\right)-24=t^2+2t-24=t^2-4t+6t-24=t\left(t-4\right)+6\left(t-4\right)=\left(t-4\right)\left(t+6\right)\)
\(=\left(x^2+5x+4-4\right)\left(x^2+5x+4+6\right)=x\left(x+5\right)\left(x^2+5x+10\right)\)
\(x^7+x^5+x^4+x^3+x^2+1\)
\(=\left(x^7+x^4\right)+\left(x^5+x^2\right)+\left(x^3+1\right)\)
\(=x^4\left(x^3+1\right)+x^2\left(x^3+1\right)+\left(x^3+1\right)\)
\(=\left(x^3+1\right)\left(x^4+x^2+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)\left(x^4+x^2+1\right)\)
a)\(3x^2-11x+6=3x^2-9x-2x+6=3x\left(x-3\right)-2\left(x-3\right)=\left(3x-2\right)\left(x-3\right)\)
b)\(8x^2+10x-3=8x^2+12x-2x-3=4x\left(2x+3\right)-\left(2x+3\right)=\left(4x-1\right)\left(2x+3\right)\)
c)\(8x^2-2x-1=8x^2+2x-4x-1=2x\left(4x+1\right)-\left(4x+1\right)=\left(2x-1\right)\left(4x+1\right)\)
x(x+2)+x(x-3)-3(x+2)
=x(x+2)-3(x+2)+x(x-3)
=(x-3)(x+2)+x(x-3)
=(x-3)(2x+2)
=2(x-3)(x+2)
Ta có : x4 + x3 + 6x2 + 5x + 5
= (x4 + 5x2) + (x3 + 5x) + (x2 + 5)
= x2(x2 + 5) + x(x2 + 5) + (x2 + 5)
= (x2 + 5)(x2 + x + 1)
\(P=\left(x-5\right)^3-x\left(x+2\right)\left(x-3\right)\)
\(P=x^3-15x^2+75x-125-x^3+3x^2-2x^2+6x\)
\(P=-14x^2+81x-125\)
Chúc bạn học giỏi