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4x2 - 36x + 56
= 4x2 - 28x - 8x + 56
= ( 4x2 - 28x ) - ( 8x - 56 )
= 4x( x - 7 ) - 8( x - 7 )
= ( x - 7 )( 4x - 8 )
= 4( x - 7 )( x - 2 )
\(4x^2-36x+56=0\)
\(\Rightarrow4\left(x^2-9x+14\right)=0\)
\(\Rightarrow4\left(x^2-7x-2x+14\right)=0\)
\(\Rightarrow4x\left(x-2\right)-7\left(x-2\right)=0\)
\(\Rightarrow4\left(x-7\right)\left(x-2\right)=0\)
\(\Rightarrow\left(x-7\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow x=7;x=2\).
\(4x^2-36x+56=0\)
\(\Leftrightarrow\left(2x\right)^2-2\cdot2x\cdot9+9^2-25=0\)
\(\Leftrightarrow\left(2x-9\right)^2-25=0\)
\(\Leftrightarrow\left(2x-9\right)^2=25\Leftrightarrow\left[{}\begin{matrix}2x-9=5\\2x-9=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=2\end{matrix}\right.\)
Vậy....................
4x2 - 36x + 56
= 4(x2 - 9x + 14)
= 4(x2 - 2x - 7x + 14)
= 4[x(x - 2) - 7(x - 2)]
= 4(x - 2)(x - 7)
\(4x^2\)−36x+56=04x2−36x+56
⇒4(x2−9x+14)=0⇒4(x2−9x+14)
⇒4(x2−7x−2x+14)=0⇒4(x2−7x−2x+14)
⇒4x(x−2)−7(x−2)=0⇒4x(x−2)−7(x−2)
⇒4(x−7)(x−2)=0⇒4(x−7)(x−2)
⇒(x−7)(x−2)=0⇒(x−7)(x−2)
⇒[x−7=0x−2=0⇒[x−7=0x−2=0
⇒x=7;x=2⇒x=7;x=2.
a) a3 - a2c + a2b - abc
= a( a2 - ac + ab - bc )
= a[ ( a2 + ab ) - ( ac + bc ) ]
= a( a( a + b ) - c( a + b ) ]
= a( a + b )( a - c )
b) ( x2 + 1 )2 - 4x2
= ( x2 + 1 )2 - ( 2x )2
= ( x2 - 2x + 1 )( x2 + 2x + 1 )
= ( x - 1 )2( x + 1 )2
c) x2 - 10x - 9y2 + 25
= ( x2 - 10x + 25 ) - 9y2
= ( x - 5 )2 - ( 3y )2
= ( x - 3y - 5 )( x + 3y - 5 )
d) 4x2 - 36x + 56
= 4x2 - 8x - 28x + 56
= 4x( x - 2 ) - 28( x - 2 )
= 4( x - 2 )( x - 7 )
bạn viết sai dấu ở câu f phải laf4x^2-8x-28x+56 mà bạn ra đc kết quả đúng
a) (x - 1)(x - 2). b) 4(x - 2)(x - 7).
c) (x + 2)(2x +1). d) (x - l)(2x - 7).
e) (2x + 3y - 3)(2x - 3y +1). g) (x - 3)( x 3 + x 2 - x +1).
h) (x + y)(x + y-l)(x + y + l).
\(x^4+x^2-2=x^4-x^2+2x^2-2 \)
\(=x^2\left(x^2-1\right)+2\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+2\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(x^2+2\right)\)
Phân tích đa thức thành nhân tử
a) 4x2-36x+56 = 4\(x^2\)-36x+81-25 = \(\left(2x\right)^2\)-2.2x.9+\(9^2\) - 25 = \(\left(2x-9\right)^2\)-\(5^2\) = ( 2x - 9 - 5 ).( 2x - 9 + 5 ) = ( 2x - 14 ).( 2x - 4 )
b ) x4+4x2 = \(x^2.\left(x^2+4\right)\)
c ) x4 + x2 +1 = \(x^2\left(x^2+2\right)\)
d) 64\(x^4+1\)=\(64\left(x^4+1\right)\)
e ) 81x4+1=\(81\left(x^4+1\right)\)
=4x2 -36x + 56
= 4x2 -8x - 28x +56
= 4x (x-2) -28 (x-2)
= (4x-28)(x-2)
= 4(x-7)(x -2)