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\(\left(5x^2-2x\right)^2+2x-5x^2-6=25x^4-2.5x^2.2x+4x^2+2x-5x^2-6.\)
\(=25x^4-20x^3-x^2+2x-6\)
\(=25x^4-25x^3+5x^3-5x^2+4x^2-4x+6x-6.\)
\(=\left(25x^4-25x^3\right)+\left(5x^3-5x^2\right)+\left(4x^2-4x\right)+\left(6x-6\right).\)
\(=25x^3\left(x-1\right)+5x^2\left(x-1\right)+4x\left(x-1\right)+6\left(x-1\right).\)
\(=\left(x-1\right)\left(25x^3+5x^2+4x+6\right)\)
\(=\left(x-1\right)\left[25x^3+15x^2-10x^2-6x+10x+6\right]\)
\(=\left(x-1\right)\left[5x^2\left(5x+3\right)-2x\left(5x+3\right)+2\left(5x+3\right)\right]\)
\(=\left(x-1\right)\left(5x+3\right)\left(5x^2-2x+2\right)\)
a) \(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=3x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\)
Dễ mà:
f(x)=(2x4-2x3)-(3x3-3x2)-(8x2-8x)-(3x-3)
=2x3(x-1)-3x2(x-1)-8x(x-1)-3(x-1)
=(x-1)(2x3-3x2-8x-3)
=(x-1)[(2x3+2x2)-(5x2+5x)-(3x+3)]
=(x-1)[2x2(x+1)-5x(x+1)-3(x+1)]
=(x-1)(x+1)(2x2-5x-3)
=(x-1)(x+1)[2x(x-3)+(x-3)]
=(x-1)(x+1)(x-3)(2x+1)
\(f\left(x\right)=2x^4-5x^3-5x^2+5x+3.\)
\(=\left(2x^4-2x^3\right)-\left(3x^3-3x^2\right)-\left(8x^2-8x\right)-\left(3x-3\right)\text{ }\left(\text{Hơi khó hiểu thông cảm! }\right)\)
\(=2x^3\left(x-1\right)-3x^2\left(x-1\right)-8x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(2x^3-3x^2-8x-3\right)\)
\(=\left(x-1\right)\left[\left(2x^3+2x^2\right)-\left(5x^2+5x\right)-\left(3x+3\right)\right]\)
\(=\left(x-1\right)\left[2x^2\left(x+1\right)-5x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=\left(x-1\right)\left(x+1\right)\left(2x^2-5x-3\right)\)
\(=\left(x-1\right)\left(x+1\right)\left[\left(2x^2-6x\right)+\left(x-3\right)\right]\)
\(=\left(x-1\right)\left(x+1\right)\left(x-3\right)\left(2x+1\right)\)
2x2-5x-2y2-5y
=2(x2-y2)-5(x+y)
=2(x+y)(x-y)-5(x+y)
=(x+y)(2x-2y-5)
\(2x^2\left(x-1\right)+3x^2-3x-2x+2.\)
\(2x^2\left(x-1\right)+3x\left(x-1\right)-2\left(x-1\right)\)
\(\left(x-1\right)\left(2x^2+3x-2\right)\)
\(2\left(x-1\right)\left(x^2+\frac{3}{2}x-2\right)=2\left(x-1\right)\left\{\left(x^2+\frac{2x.3}{4}+\frac{9}{16}\right)-\left(2+\frac{9}{16}\right)\right\}\)
\(2\left(x-1\right)\left\{\left(x+\frac{3}{4}\right)^2-\left(2+\frac{9}{16}\right)\right\}=2\left(x-1\right)\left\{\left(x+\frac{3}{4}-2-\frac{9}{16}\right)\left(x+\frac{3}{4}+2+\frac{9}{16}\right)\right\}\)
\(=2x^3+4x^2-3x^2-6x+x+2\)
= \(2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\)
= \(\left(x+2\right)\left(2x^2-3x+1\right)\)
= \(\left(x+2\right)\left(2x^2-x-2x+1\right)\)
= \(\left(x+2\right)\left(2x\left(x-1\right)-\left(x-1\right)\right)\)
= \(\left(x+2\right)\left(x-1\right)\left(2x-1\right)\)
P = x3 - x2 - x2 + x + 4x - 4 = x2(x-1) - x(x - 1) + 4(x-1) = (x - 1)(x2 - x + 4).
Hết, đa thức bậc 2: x2 - x + 4 ko phân tích được thành nhân tử.
a) \(45+x^3-5x^2-9x\)
\(\Leftrightarrow\left(45-9x\right)+\left(x^3-5x^2\right)\)
\(\Leftrightarrow-9\left(x-5\right)+x^2\left(x-5\right)\)
\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\left(x+3\right)\)
TK NKA !!!
\(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+x+2\)
\(=\left(x+2\right)\left(2x+1\right)\)
2x2 + 5x + 2
= 2x2 + 4x + x + 2
= (2x2 + 4x) + (x + 2)
= 2x (x + 2) + (x + 2)
= (2x + 1) (x + 2)