t.i.c.k mik mik t.i.c.k lại

x^2 + 7x -15

= x^2 + 7x +12,25  -27,25

= (x+3,5)^2 - 27, 25

= ( x+3,5 - \(\sqrt{27,25}\))(x+3,5+\(\sqrt{27,25}\))

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)

\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)

\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)

\(a.x^3+3x^2+4x+2\)

\(=x^3+x^2+2x^2+2x+2\)

\(=x^2\left(x+1\right)+2x\left(x+1\right)+2\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+2x+2\right)\)

\(b.6x^4-x^3-7x^2+x+1\)

\(=6x^4-6x^3+5x^3-5x^2-2x^2+2x-x+1\)

\(=6x^3\left(x-1\right)+5x^2\left(x-1\right)-2x\left(x-1\right)-\left(x-1\right)\)

\(=\left(x-1\right)\left(6x^3+5x^2-2x-1\right)\)

\(=\left(x-1\right)\left(6x^3+6x^2-x^2-x-x-1\right)\)

\(=\left(x-1\right)\left[6x^2\left(x+1\right)-x\left(x+1\right)-\left(x+1\right)\right]\)

\(=\left(x-1\right)\left(x+1\right)\left(6x^2-x-1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(6x^2-3x+2x-1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left[3x\left(2x-1\right)+\left(2x-1\right)\right]\)

\(=\left(x-1\right)\left(x+1\right)\left(2x-1\right)\left(3x+1\right)\)

k giùm cái cho đỡ buồn!

\(x^4-4x^3-7x^2+22x+24\)

\(=\left(x^4-4x^3\right)-\left(7x^2-28x\right)-\left(6x-24\right)\)

\(=x^4.\left(x-4\right)-7x.\left(x-4\right)-6.\left(x-4\right)\)

\(=\left(x-4\right).\left(x^4-7x-6\right)\)

Tham khảo nhé~

\(b,4x^2-x-5=0\)

\(\Leftrightarrow4x^2-5x+4x-5=0\)

\(\Leftrightarrow x\left(4x-5\right)+4x-5=0\)

\(\Leftrightarrow\left(4x-5\right)\left(x+1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=-1\\x=\frac{5}{4}\end{cases}}\)

Bài 2

\(a,x^3+5x^2+3x-9\)

\(\Leftrightarrow x^3-x^2+6x^2-6x+9x-9\)

\(\Leftrightarrow x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)

\(\Leftrightarrow\left(x-1\right)\left(x^2+6x+9\right)\)

\(\Leftrightarrow\left(x-1\right)\left(x+3\right)^2\)

b,\(x^3-7x-6\)

\(\Leftrightarrow x^3-3x^2+3x^2-9x+2x-6\)

\(\Leftrightarrow x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x^2+3x+2\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)\)

c,\(3x^3-7x^2+17x-5\)

\(\Leftrightarrow3x^3-x^2-6x^2+2x+15x-5\)

\(\Leftrightarrow x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)

\(\Leftrightarrow\left(3x-1\right)\left(x^2-2x+5\right)\)

\(4x^2-x-5=0\)

<=>  \(4x^2+4x-5x-5=0\)

<=>   \(4x\left(x+1\right)-5\left(x+1\right)=0\)

<=>  \(\left(x+1\right)\left(4x-5\right)=0\)

tự lm tiếp

Bài 1:

a)\(28x^3+15x^2+75x+125=0\)

\(\Leftrightarrow\left(4x+5\right)\left(7x^2-5x+25\right)=0\)

Dễ thấy: \(7x^2-5x+25=7\left(x-\frac{5}{14}\right)^2+\frac{675}{28}>0\)

\(\Rightarrow4x+5=0\Rightarrow x=-\frac{5}{4}\)

b)\(4x^2-x-5=0\)

\(\Leftrightarrow\left(x+1\right)\left(4x-5\right)=0\)

\(\Rightarrow x=-1;x=\frac{5}{4}\)

Bài 2:

a)\(x^3+5x^2+3x-9\)

\(=\left(x-1\right)\left(x+3\right)^2\)

b)\(x^3-7x-6\)

\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\)

c)\(3x^3-7x^2+17x-5\)

\(=\left(3x-1\right)\left(x^2-2x+5\right)\)

\(4x^2-x-5=0\)

<=> \(4x^2+4x-5x-5=0\)

<=>  \(4x\left(x+1\right)-5\left(x+1\right)=0\)

<=>  \(\left(x+1\right)\left(4x-5\right)=0\)

tự giải nốt

\(1-3x-x^3+3x^2\)\(=\left(1-x^3\right)+\left(3x^2-3x\right)\)

\(=\left(1-x\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)

\(=\left(x-1\right)\left(3x-x^2-x-1\right)=\left(x-1\right)\left(2x-x^2-1\right)\)