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x2-x-12=x2+3x-4x-12=(x2+3x)-(4x+12)=x(x+3)-4(x+3)=(x+3)(x-4)
\(x^3+x^2+4=x^3+2x^2-x^2-2x+2x+4\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x^2-x+2\right)\left(x+2\right)\)
\(x^8+64=x^8+16x^4+64-16x^4\)
\(=\left(x^4+8\right)^2-\left(4x^2\right)^2\)
\(=\left(x^4-4x^2+8\right)\left(x^4+4x^2+8\right)\)
\(4a^4+b^4=4a^4+4a^2b^2+b^4-4a^2b^2\)
\(=\left(2a^2+b^2\right)^2-\left(2ab\right)^2\)
\(=\left(2a^2+b^2-2ab\right)\left(2a^2+b^2+2ab\right)\)
\(x^3-2x-4=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2x+2\right)\left(x-2\right)\)
Chúc bạn học tốt.
1)7x(x-5)-x(x-5)=(x-5)(7x-x)=6x(x-5)
2)x4+3x3+x+3=x3(x+3)+(x+3)=(x+3)(x3+1)=(x+3)(x+1)(x2-x+1)
3)x4+64=[(x2)2+2.x2.8+64]-16x2=(x2+8)2-(4x)2=(x2+4x+8)(x2-4x+8)
a) x3-3x+2= x3-1-3x+3= (x-1)(x2+x+1)-3(x-1)= (x-1)(x2+x+1-3)= (x-1)(x2+x-2)
c,x8+x7+x6+x5+x4+x3+x2+x+1
=(x8+x7+x6)+(x5+x4+x3)+(x2+x+1)
=x6(x2+x+1)+x3(x2+x+1)+(x2+x+1)
=(x2+x+1)(x6+x3+1)
a) \(-5x^2+16x-3=-5x^2+15x+x-3=-5x\left(x-3\right)+x-3=\left(x-3\right)\left(1-5x\right).\)
b) \(x^4+64=x^4+16x^2+64-16x^2=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2+4x+8\right)\left(x^2-4x+8\right).\)
c) \(64x^2+4y^4=4\left(16x^2+y^4\right)\)
d) \(x^5+x-1\)đa thức này có nghiệm vô tỷ. Mik ko phân tích được.
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)
\(x^2-x-12\)
\(=x^2-x-12\)
\(=\left(x-4\right)\left(x+3\right)\)