\(a,3x^2+2x-1\)
\(\Leftrightarrow3x^2+3x-x-1\)
\(\Leftrightarrow3x\left(x+1\right)-\left(x+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-1\right)\)
\(b,x^3+6x^2+11x+6\)
\(\Leftrightarrow x^3+3x^2+3x^2+9x+2x+6\)
\(\Leftrightarrow x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+6\right)\)
\(\Leftrightarrow\left(x+3\right)\left(x^2+3x+2\right)\)
\(\Leftrightarrow\left(x+3\right)\left(x+1\right)\left(x+2\right)\)
\(c,x^4+2x^2-3\)
\(\Leftrightarrow x^4-x^3+x^3-x^2+3x^2-3\)
\(\Leftrightarrow x^3\left(x-1\right)+x^2\left(x-1\right)+3\left(x-1\right)\left(x+1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+x^2+3x+3\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+3\right)\)
\(d,ab+ac+b^2+2bc+c^2\)
\(\Leftrightarrow a\left(b+c\right)+\left(b+c\right)^2\)
\(\Leftrightarrow\left(b+c\right)\left(a+b+c\right)\)
3x^2+2x-1=3x^2+3x-x-1=3x(x+1)-(x+1)=(x+1)(3x-1)
x^4+2x^2-3=x^4+3x^2-x^2 -3=x^2(x^2+3)-(x^2+3)=(x^2+3)(x^2-1)
a) \(3x^2+2x-1=3x^2+3x-x\)\(-1\)
\(3x\left(x+1\right)-\left(x+1\right)\)
\(=\left(3x-1\right)\left(x+1\right)\)
b) x3 + 6x2 + 11x + 6 = x3+6x2+12x+8-x-2 = ( x3+6x2+12x+8)-(x+2) = (x+2)^3 - (x+2) = (x+2)[(x+2)^2 - 1]
=(x+2)(x^2 +4x + 4 - 1) = (x+2)(x^2 + 4x +3)
c) x4 + 2x2 – 3 = x4 + 2x2 +1 - 4 = (x^2 +1)^2 - 2^2
= (x^2 + 1 + 2)(x^2 + 1- 2)
=(x^2 + 3)( x^2 - 1)
ab + ac +b2 + 2bc + c2= a(b+c) + (b+c)^2
=(b+c)(a+b+c)
a3 – b3 + c3 + 3abc\(=a^3-3a^2b+3ab^2-b^3+3a^2b-3ab^2+c^3+3abc\)
\(=\left(a-b\right)^3+3ab\left(a-b\right)+c^3+3abc\)
\(=\left[\left(a-b\right)^3+c^3\right]+\left[3ab\left(a-b\right)+3abc\right]\)
\(=\left(a-b+c\right)\left[\left(a-b\right)^2-\left(a-b\right)c+c^2\right]\)\(+3ab\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(a^2-2ab+b^2-ac+bc+c^2\right)\)\(+3ab\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(a^2-2ab+b^2-ac+bc+c^2+3ab\right)\)
\(=\left(a-b+c\right)\left(a^2+b^2+c^2-ac+bc+ab\right)\)
câu cuối ko bik đúng hay sai đâu nha
