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1a.

$x^2-5x+6=x^2-2x-(3x-6)=x(x-2)-3(x-2)=(x-2)(x-3)$

1b.

$3x^2+9x-30=3(x^2+3x-10)=3(x^2-2x+5x-10)$

$=3[x(x-2)+5(x-2)]=3(x-2)(x+5)$

1c.
$x^2-3x+2=(x^2-x)-(2x-2)=x(x-1)-2(x-1)=(x-1)(x-2)$

1d.

$x^2-9x+18=x^2-3x-(6x-18)=x(x-3)-6(x-3)=(x-3)(x-6)$

1e.

$x^2-6x+8=x^2-2x-(4x-8)=x(x-2)-4(x-2)=(x-2)(x-4)$

1f.
$x^2-5x-14=x^2-7x+2x-14=x(x-7)+2(x-7)=(x+2)(x-7)$

1g.

$x^2+6x+5=(x^2+x)+(5x+5)=x(x+1)+5(x+1)=(x+1)(x+5)$

1h.

$x^2-7x+12=x^2-3x-(4x-12)=x(x-3)-4(x-3)=(x-3)(x-4)$

1i.

$x^2-7x+10=(x^2-2x)-(5x-10)=x(x-2)-5(x-2)=(x-2)(x-5)$

2a.

$3x^2-5x-2=(3x^2-6x)+(x-2)=3x(x-2)+(x-2)$

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

2b. 

$2x^2+x-6=(2x^2+4x)-(3x+6)=2x(x+2)-3(x+2)$

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

2c.

$7x^2+50x+7=(7x^2+49x)+(x+7)$

$=7x(x+7)+(x+7)=(7x+1)(x+7)$

2d. 

$12x^2+7x-12=(12x^2-9x)+(16x-12)$

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

2e.

$15x^2+7x-2=15x^2-3x+10x-2$

$=3x(5x-1)+2(5x-1)=(5x-1)(3x+2)$

6: Chiều rộng hình chữ nhật là:

42,5:2=21,25(m)

Diện tích hình chữ nhật là:

\(42,5\times21,25=903,125\left(m^2\right)\)

7:

38,9x2,32

847,91-91

564,3-19

266,7:10,5=2667:105

Bài 4:

a: \(x\times4,3=22,704\)

=>x=22,704:4,3=5,28

b: \(x:8,16=2,73\)

=>\(x=2,73\times8,16=22,2768\)

Bài 3:

a: 37,2-37,2:5

=37,2-7,44

=29,76

b: 649x84,5+17

=54840,5+17

=54857,5

g) \(\left\{{}\begin{matrix}x-1\ge0\\2-\sqrt{x-1}\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\\sqrt{x-1}\le2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\-4\le x-1\le4\end{matrix}\right.\)

\(\Leftrightarrow1\le x\le5\)

h) \(\left\{{}\begin{matrix}\dfrac{2x-4}{5-x}\ge0\\5-x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-4\ge0\\5-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-4\le0\\5-x< 0\end{matrix}\right.\end{matrix}\right.\\x\ne5\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}5>x\ge2\left(tm\right)\\5< x\le2\left(vl\right)\end{matrix}\right.\\x\ne5\end{matrix}\right.\)

\(\Leftrightarrow5>x\ge2\)

i) \(x^2-8x-9\ge0\)\(\Leftrightarrow\left(x-4\right)^2-25\ge0\Leftrightarrow\left(x-4\right)^2\ge25\)

\(\Leftrightarrow-5\ge x-4\ge5\)\(\Leftrightarrow-1\ge x\ge9\)

j) \(2x-x^2>0\)

\(\Leftrightarrow\left(x-1\right)^2< 1\)

\(\Leftrightarrow-1< x-1< 1\Leftrightarrow0< x< 2\)

a: ĐKXĐ: \(2\le x\le4\)

b: ĐKXĐ: x>0

c: ĐKXĐ: \(x< \dfrac{1}{3}\)

g: ĐKXĐ: \(1\le x\le4\)

h: ĐKXĐ: \(2\le x< 5\)

i: ĐKXĐ: \(\left[{}\begin{matrix}x\ge9\\x\le-1\end{matrix}\right.\)

\(0< x< 2\)

Câu 19: B

Câu 20: A

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