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\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
\(x^4-5x^2+4\)
=\(\left(x^4-x^2\right)-\left(4x^2-4\right)\)
=\(x^2\left(x^2-1\right)-4\left(x^2-1\right)\)
=\(\left(x^2-4\right)\left(x^2-1\right)\)
\(x^2+5x-6\)
=\(x^2-x+6x-6\)
=\(x\left(x-1\right)+6\left(x-1\right)\)
=\(\left(x+6\right)\left(x-1\right)\)
2 câu cuối làm tương tự nha câu 2 nha
đặt a=x^2-5x
(x^2-5x)^2+10(x^2-5x+24)
=a^2+10(a+24)
=a^2+10a+24
=a^2+6a+4a+24
=a(a+6)+4(a+6)
=(a+6)(a+4)
=(x^2-5x+6)(x^2-5x+4)
=[x^2-3x-2x+6][x^2-x-4x+4]
=[x(x-3)-2(x-3)][x(x-1)+4(x-1)]
=(x-3)(x-2)(x-1)(x+4)
1. \(x\left(x^2-5xy-14y^2\right)=x\left(x^2-7xy+2xy-14y^2\right)\)
\(=x\left(x-2\right)\left(x-7\right)\)
2. \(x^4+2x^2+1-9x^2=\left(x^2+1\right)^2-\left(3x\right)^2=\left(x^2+1-3x\right)\left(x^2+1+3x\right)\)
3. \(4x^4+4x^2+1-16x^2=\left(2x^2+1\right)^2-\left(4x\right)^2=\left(2x^2-4x+1\right)\left(2x^2+4x+1\right)\)
4. \(x^2+x+7x+7=\left(x+7\right)\left(x+1\right)\)
5. \(x\left(x^2-5x-14\right)=x\left(x^2-7x+2x-14\right)=x\left(x+2\right)\left(x-7\right)\)
Phân tích đa thức thành nhân tử :
1.x3-5x2y-14xy2
2.x4-7x2+1
3.4x4-12x2+1
4.x2+8x+7
5.x3-5x2-14x
\(x^4+5x^3-12x^2+5x+1\)
\(=x^4-x^3+6x^3-6x^2-6x^2+6x-x+1\)
\(=x^3\left(x-1\right)+6x^2\left(x-1\right)-6x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+6x^2-6x-1\right)\)
\(=\left(x-1\right)\left(x^3-x^2+7x^2-7x+x-1\right)\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)+7x\left(x-1\right)+\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x^2+7x+1\right)\)
\(x^4-5x^2+4=x^4-x^2-4x^2+4=x^2\left(x^2-1\right)-4\left(x^2-1\right)=\left(x^2-4\right)\left(x^2-1\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)=\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
Ta có : x4 - 5x2 + 4
= x4 - x2 - 4x2 + 4
= x2(x2 - 1) + (4x2 - 4)
= x2(x2 - 1) + 4(x2 - 1)
= (x2 - 1)(x2 + 4)
x4 + x3 + 6x2 + 5x + 5
=x4+x3+x2+5x2+5x+5
=x2.(x2+x+1)+5.(x2+x+1)
=(x2+x+1)(x2+5)
\(A=\left(x^2-5x-4\right)^2+7\left(x^2-5x-4\right)+10\)
Đặt \(t=x^2-5x-4\).
\(A=t^2+7t+10=t^2+2t+5t+10=\left(t+2\right)\left(t+5\right)\)
\(=\left(x^2-5x-4+2\right)\left(x^2-5x-4+5\right)\)
\(=\left(x^2-5x-2\right)\left(x^2-5x+1\right)\)