Bài 1: phân tích đa thức sau thành nhân tử: a) 5x3 - 45x b) a3 - 8 + 6a2 -12a c) ( a + b )3 + ( a – b )3 d) x ( 2x – 7 ) ( 4x – 14 ) e) x4 + 3x3 – 9x – 9 Bài 2: tìm x: a) 2x3 – 50x =0 b) x3 – 16x = 0 c) 7x ( x – 2004 ) – x + 2004 = 0 d) 5x ( x – 3 ) + 7 ( x + 3 ) = 0

Đáp án + Giải thích các bước giải:

Bài `1`:

` a) 5x³-45x`

`=5x(x²-9)`

`=5x(x-3)(x+3)`

`b) a³-8+6a²-12a`

`=(a-2)(a²+2a+b²)+6a(a-2)`

`=(a-2)(a²+8a+b²)`

`c) (a+b)³+(a-b)³` `=a³+3a²b+3ab²+b³+a³-3a²b+3ab²-b³`

`=2a³+6ab²`

`=2a²(a+3b²)`

`d)x ( 2x – 7 )( 4x – 14 )`

Sửa đề:

`x ( 2x – 7 )+ ( 4x – 14 )`

`=x ( 2x – 7 )+2(2x-7)`

`=(2x-7)(x+2)`

`e)x^4+3x³-9x-9`

` =x^4-3²+3x(x²-3)`

`=(x²-3)(x²+3)+3x(x²-3)`

`=(x²-3)(x²+3x+3)`

Bài `2`:

`a)2x³-50x=0`

`⇔2x(x²-25)=0`

`⇔2x(x-5)(x+5)=0`

`=>`\(\left[ \begin{array}{l}2x=0\\x-5=0\\x+5=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=0\\x=5\\x=-5\end{array} \right.\)

`b)x³-16x=0`

`⇔x(x²-16)=0`

`⇔x(x-4)(x+4)=0`

`=>`\(\left[ \begin{array}{l}x=0\\x-4=0\\x+4=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0\\x=4\\x=-4\end{array} \right.\)

`c)7x ( x – 2004 ) – x + 2004 = 0`

`⇔7x(x-2004)-(x-2004)=0`  

`⇔(7x-1)(x-2004)=0`

`=>`\(\left[ \begin{array}{l}7x-1=0\\x-2004=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{7}\\x=2004\end{array} \right.\)

`d)5x ( x – 3 ) + 7x ( x + 3 ) = 0`

`⇔5x²-15x+7x²+21x=0`

`⇔12x²+6x=0`

`⇔6x(2x+1)=0`

`=>`\(\left[ \begin{array}{l}6x=0\\2x+1=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{-1}{2}\end{array} \right.\)