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\(x^3-2x^2-5x+6\)
\(=\left(x^3-4x^2+3x\right)+\left(2x^2-8x+6\right)\)
\(=x\left(x^2-4x+3\right)+2\left(x^2-4x+3\right)\)
\(=\left(x+2\right)\left(x^2-4x+3\right)\)
1. \(x^3-2x-5x+6\)
\(\Leftrightarrow x^2\left(x-3\right)+x\left(x-3\right)-2\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+x-2\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)\left(x-1\right)\)
2. \(x^3-7x^2+15x-9\)
\(\Leftrightarrow\left(x^3-x^2\right)-\left(6x^2-6x\right)+\left(9x-9\right)\)
\(\Leftrightarrow x^2\left(x-1\right)-6x\left(x-1\right)+9\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-6x+9\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x\left(x-3\right)-3\left(x-3\right)\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)^2\)
a) co sai de ko
b)x3-2x2+4x2-8x+3x-6=x2(x-2)+4x(x-2)+3(x-2)=(x-2)(x2+4x+3)=(x-2)(x+3)(x+1)
c)x3-2x2+2x2-4x-3x+6=x2(x-2)+2x(x-2)-3(x-2)=(x-2)(x2+2x-3)=(x-2)(x+3)(x-1)
d)x3-3x2+x2-3x-2x+6=x2(x-3)+x(x-3)-2(x-3)=(x-3)(x2+x-2)=(x-3)(x+2)(x-1)
1/ \(2x^2+3x-5=\left(2x^2+2x\right)-\left(5x+5\right)=2x\left(x+1\right)-5\left(x+1\right)=\left(x+1\right)\left(2x-5\right)\)
2/ \(16x-5x^2-3=\left(15x-5x^2\right)+\left(x-3\right)=5x\left(3-x\right)-\left(3-x\right)=\left(3-x\right)\left(5x-1\right)\)
3/ \(7x-6x^2-2=\left(3x-6x^2\right)-\left(2-4x\right)=3x\left(1-2x\right)-2\left(1-2x\right)=\left(1-2x\right)\left(3x-2\right)\)
4/ \(x^2+5x-6=\left(x^2-x\right)+\left(6x-6\right)=x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x+6\right)\)
\(x^3+2x-3\)
\(=x^3-x+3x-3\)
\(=x\left(x^2-1\right)+3\left(x-1\right)\)
\(=x\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x\left(x+1\right)+3\right)\)
\(x^3+5x^2+8x+4\)
\(=\left(x+1\right)\left(x+2\right)\)
Cây cuối tương tự câu đầu thôi:
\(x^3-7x+6\)
\(=x^3-x-6x+6\)
.......
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
a) Ta có : x2 + 7x + 12
= x2 + 3x + 4x + 12
= (x2 + 3x) + (4x + 12)
= x(x + 3) + 4(x + 3)
= (x + 4)(x + 3)
Bạn ơi mk nhầm đề rồi số 30 thay bằng số 60 còn 36 thay bằng 72 và 39 thay bằng 75 nha
a)x2+5x-6
=x2+6x-x-6
=x(x+6)-(x+6)
=(x-1)(x+6)
b)7x-6x2-2
=-6x2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
c)x2+4x+3
=x2+3x+x+3
=x(x+3)+(x+3)
=(x+1)(x+3)
d)2x2+3x-5
=2x2+5x-2x-5
=x(2x+5)-(2x+5)
=(x-1)(2x+5)
\(1,x^2+5x-6=x^2-x+6x-6=x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x+6\right)\)
\(3,7x-6x^2-2=-6x^2+7x-2=-6x^2+3x+4x-2=3x\left(-2x+1\right)+2\left(2x-1\right)\)
\(=3x\left(1-2x\right)-2\left(1-2x\right)=\left(1-2x\right)\left(3x-2\right)\)
\(2,5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(5x-1\right)\)
A = x2 - 7x + 6
=(x-1)(x-6)
cũng dễ thôi mà!!!
a, \(x^2-7x+6=x^2-x-6x+6\)
\(=x\left(x-1\right)-6\left(x-1\right)\)
\(=\left(x-6\right)\left(x-1\right)\)
b, \(|2x+1|-5x=3\)(*)
TH1: \(2x+1\ge0=>x\ge\frac{-1}{2}\)
PT(*) <=> \(2x+1-5x=3=>x=\frac{-2}{3}\)(thỏa mãn)
TH2: \(2x+1< 0=>x< \frac{-1}{2}\)
PT(*) <=> \(-2x-1-5x=3=>x=\frac{4}{7}\)(ko thỏa mãn)
Vậy phương trình có tập nghiệm S=\(\left\{\frac{-2}{3}\right\}\)