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\(a,x^2-5=x^2-\left(\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)
\(b,x^4+x^3+x+1=x^3.\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right).\left(x^3+1\right)=\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
\(c,x^3-19x-30=x^3-25x+6x-30\)
\(=x.\left(x^2-25\right)+6.\left(x-5\right)\)
\(=x.\left(x-5\right)\left(x+5\right)+6.\left(x-5\right)\)
\(=\left(x-5\right).\left[x\left(x+5\right)+6\right]\)
\(=\left(x-5\right).\left(x^2+5x+6\right)\)
\(=\left(x-5\right).\left(x^2+2x+3x+6\right)\)
\(=\left(x-5\right)\left[x.\left(x+2\right)+3.\left(x+2\right)\right]\)
\(=\left(x-5\right)\left(x+2\right)\left(x+3\right)\)
\(a,x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2+5\right)\left(x^2-1\right)\)
a) x3−19x−30=(x−5)(x+2)(x+3)
b) x4−x2+1=x4+2x2+1−3x2=(x2+1)2−(x√3)2=(x2+1+x√3)(x2+1−x√3)
a)( x3 -19x-30=(x-5)(x+2)(x+3)
b) 2x3 -5x2+8x-3=(2x-1)(x2-2x+3)
\(a\text{) }x^3-19x-30=\left(x-5\right)\left(x+2\right)\left(x+3\right)\)
\(b\text{) }x^4-x^2+1=x^4+2x^2+1-3x^2=\left(x^2+1\right)^2-\left(x\sqrt{3}\right)^2=\left(x^2+1+x\sqrt{3}\right)\left(x^2+1-x\sqrt{3}\right)\)
a)9(2x+1)2 - 4(x-1) 2
<=>33(2x+1)2-22(x+1)2
<=>(3(2x+1)) 2-(2(x+1))2
<=>(6x+3)2-(2x+1)2
<=>((6x+3)-(2x+1)) ((6x+3)+(2x+1))
<=>(6x+3-2x-1)(6x+3+2x+1)
<=.>(4x+2)(8x+4)
b) x3 - 19x- 30
<=>x3-25x+6x-30
<=.>x(x2-52)+6(x-5)
<=>x(x+5)(x-5)+6(x-5)
<=>(x-5) (x2+5x+6)
<=>(x-5) (x2+2x+3x+6)
<=>(x-5) ( x(x+2)+3(x+2))
<=>(x-5) (x+2)(x+3)
c) x4+ x2 +1
<=>x4+x2+1
<=>x4−x+x2+x+1
<=>x(x3−1)+(x2+x+1)
<=>x(x−1)(x2+x+1)+(x2+x+1)
<=>(x2+x+1)[x(x−1)+1]
<=>(x2+x+1)(x2−x+1)
câu d mình chịu :(((
a) 4x*(x+y)*(x+y+z)*(x+z)+y^2+z^2
=4*x*y*z^2+4*x^2*z^2+z^2+4*x*y^2*z+12*x^2*y*z+8*x^3*z+4*x^2*y^2+y^2+8*x^3*y+4*x^4
b) x^3-19x-30
=(x-5)*(x+2)*(x+3)