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[ (x+2)^2 + 5]^2 +3x^3 + 14x^2 + 24x
= (x+2)^4 + 8[(x+2)]^2 + 16 + (3x^2).(x+2) + 8x(x+2) +8x
=(x+2).[(x+2)^3 +8(x+2) + 3x^2 +8x +8 ]
=(x+2).[x^3 + 9x^2 + 28x +32 ]
=(x+2).(x+4).(x^2 +5x +8)
các bạn ơi làm ơn giải hộ mình bài này mình đang cần rất rất gấp
\(A=5x^3-125x=5x\left(x-5\right)\left(x+5\right)\)
\(B=x^3-8+\left(x-2\right)\left(5x+4\right)\)
\(=\left(x-2\right)\left(x^2+2x+4+5x+4\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x+4\right)\)
#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
Bài 1 :
\(x^2-6x+8=x^2-2x-4x+8=x\left(x-2\right)-4\left(x-2\right)=\left(x-4\right)\left(x-2\right)\)
Bài 2 :
\(x^8+x^7+1=x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1-x^6-x^5-x^4-x^3-x^2-x\)
\(=x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+x^2+x+1-x^4\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right)\left(x^6+x^3+1-x^4-x\right)\)
Tick đúng nha
a, x^2 + 2x - 8
= x^2 -2x + 4x - 8
= x(x - 2) + 4(x - 2)
= (x + 4)(x - 2)
b, x^2 + 5x + 6
= x^2 + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 3)(x + 2)
a/ \(x^2+2x-8\)
\(=x^2+4x-2x-8\)
\(=\left(x^2+4x\right)-\left(2x+8\right)\)
\(=x\left(x+4\right)-2\left(x+4\right)\)
\(=\left(x-2\right)\left(x+4\right)\)
b/ \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=\left(x^2+2x\right)+\left(3x+6\right)\)
\(=x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(x+3\right)\)
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)