c ) \(x^2-7x+12\)

\(=\left(x^2-3x\right)-\left(4x-12\right)\)

\(=x\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x-4\right)\left(x-3\right)\)

d ) \(x^2+7x+12\)

\(=\left(x^2+3x\right)+\left(4x+12\right)\)

\(=x\left(x+3\right)+4\left(x+3\right)\)

\(=\left(x+4\right)\left(x+3\right)\)

a ) \(x^2-5x+6\)

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

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

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

b )\(x^2+5x+6\)

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

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

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

a.x^2 - 5x + 6

=x²-2x-3x+6

=x(x-2)-3(x-2)

=(x-3)(x-2)

b.x^2 + 5x + 6

=x²+3x+2x+6

=x(x+3)+2(x+3)

=(x+2)(x+3)

a: =4x^2+8x-3x-6

=4x(x+2)-3(x+2)

=(x+2)(4x-3)

b: =3(3x^2-2x-1)

=3(3x^2-3x+x-1)

=3(x-1)(3x+1)

c: =2x^2-4x+x-2

=2x(x-2)+(x-2)

=(x-2)(2x+1)

d: =3x^2+3x-2x-2

=3x(x+1)-2(x+1)

=(x+1)(3x-2)

e: =3x^2+9x+x+3

=3x(x+3)+(x+3)

=(x+3)(3x+1)

a) \(4x^2+5x-6\)

\(=4x^2+8x-3x-6\)

\(=\left(4x^2+8x\right)-\left(3x+6\right)\)

\(=4x\left(x+2\right)-3\left(x+2\right)\)

\(=\left(x+2\right)\left(4x-3\right)\)

b) \(9x^2-6x-3\)

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

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

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

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

c) \(2x^2-3x-2\)

\(=2x^2-4x+x-2\)

\(=\left(2x^2-4x\right)+\left(x-2\right)\)

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

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

d) \(3x^2+x-2\)

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

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

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

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

e) \(3x^2+10x+3\)

\(=3x^2+9x+x+3\)

\(=3x\left(x+3\right)+\left(x+3\right)\)

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

x²-2.x.1/2 +(1/2)²-9/4

=(x-1/2)²-9/4

=(x-1/2)²-(3/2)²

=(x-1/2-3/2).(x-1/2+3/2)

=(x-2)(x+1)

a)x²-5x+6=(x²-2x)-(3x-6)=x(x-2)-3(x-2)(=(x-2)(x-3)

b)x²+5x+6=(x²+2x)+(3x+6)=x(x+2)+3(x+2)=(x+2)(x+3)

c)x²-7x+12=(x²-3x)-(4x-12)=x(x-3)-4(x-3)=(x-3)(x-4)

d)x²+7x+12=(x²+3x)+(4x+12)=x(x+3)+4(x+3)=(x+3)(x+4)

x² + x -12 = x² + 4x - 3x - 12 = x(x+4) - 3(x+4) = (x+4)(x-3)

\(x^2+x-12\)

\(=x^2+x+\frac{1}{4}-\frac{49}{4}\)

\(=\left(x+\frac{1}{2}\right)^2-\left(\frac{7}{2}\right)^2\)

\(=\left(x+\frac{1}{2}-\frac{7}{2}\right)\left(x+\frac{1}{2}+\frac{7}{2}\right)\)

\(=\left(x-3\right)\left(x+4\right)\)

BỔ SUNG HẰNG ĐẲNG THỨC LÀ GÌ

x^2 -x +20 =(ax +b)(cx+d)

\(1,\)

\(x^2+x-12\)

\(=x^2-3x+4x-12\)

\(=x\left(x-3\right)+4\left(x-3\right)\)

\(=\left(x+4\right)\left(x-3\right)\)

\(2,\)
\(x^2-9x+20\)

\(=x^2-4x-5x+20\)

\(=x\left(x-4\right)-5\left(x-4\right)\)

\(=\left(x-5\right)\left(x-4\right)\)

\(3,\)

\(x^2+x-20\)

\(=x^2-4x+5x-20\)

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

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

Cách 1:

Ta có: x² – x – 12 = x² – x – 16 + 4

= (x² – 16) – (x – 4)

= (x – 4).(x + 4) – (x – 4)

= (x – 4).(x + 4 – 1)

= (x – 4).(x + 3)

Cách 2:

x² – x – 12 = x² – x – 9 – 3

= (x² – 9) – (x + 3)

= (x – 3).(x + 3) – (x + 3)

= (x + 3).(x – 4)

Cách 3:

x² – x – 12 = x² – 4x + 3x – 12

= (x² – 4x) + (3x – 12)

= x.(x – 4) + 3.(x – 4)

= (x – 4).(x + 3).

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