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\(-2x^4-7x^3-x^2+7x+3\)
\(=-2x^3\left(x+1\right)-5x^2\left(x+1\right)+4x\left(x+1\right)+3\left(x+1\right)\)
\(=-\left(x+1\right)\left(2x^3+5x^2-4x-3\right)\)
\(=-\left(x+1\right)\left[2x^2\left(x-1\right)+7x\left(x-1\right)+3\left(x-1\right)\right]\)
\(=-\left(x+1\right)\left(x-1\right)\left(2x^2+7x+3\right)\)
\(=-\left(x+1\right)\left(x-1\right)\left(x+3\right)\left(2x+1\right)\)
\(x^3+7x^2y+7xy^2+y^3\)
\(\Leftrightarrow x^3+3x^2y+3xy^2+y^3+4x^2y+4xy^2\)
\(\Leftrightarrow\left(x+y\right)^3+4xy\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)\left[\left(x+y\right)^2+4xy\right]\)
\(\Leftrightarrow\left(x+y\right)\left(x^2+6xy+y^2\right)\)
P/s tham khảo nha
\(x^3+7x^2y+7xy^2+y^3\)
\(\Leftrightarrow x^3+3x^2y+3xy^2+y^3+4x^2y+4xy^2\)
\(\Leftrightarrow\left(x+y\right)^3+4xy\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)\left[\left(x+y\right)^2+4xy\right]\)
\(\Leftrightarrow\left(x+y\right)\left(x^2+6xy+y^2\right)\)
P/s tham khảo nha
\(x^3-7x-6\)
\(=x^3+2x^2-2x^2-4x-3x-6\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x^2+x-3x-3\right)\)
\(=\left(x+2\right)\left[x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x-3\right)\)
x³ -7x - 6
= x³ -x²+x²-x-6x- 6
= x²(x-1)+x(x-1)-6(x+1)
= (x-1)(x² +x) - 6(x+1)
= (x-1)x(x+1) - 6(x+1)
=(x2-x-6)(x+1)
=(x2 - 3x + 2x - 6)(x+1)
=[x(x+2)-3(x+2)](x+1)
=(x-3)(x+2)(x+1)
x³ -7x +6
= x³ -x²+x²-x-6x+6
= x²(x-1)+x(x-1)-6(x-1)
= (x-1)(x² +x-6)
= (x-1)(x²-2x+3x-6)
=(x-1)(x-2)(x+3)