Question

Bài 1: Phân tích đa thức thành nhân tử

a) \(x^2+4x+4\) b) \(6x-9-x^2\) c) \(x^2-16\) d) \(9x^2-25\)

e)\(x^4-y^4\) f) \(x^6-y^6\) g) \(8x^3-\dfrac{1}{27}\) h) \(27x^3+\dfrac{1}{64}\)

Answer 1

b) 6x - 9 - x²
= - (x² - 6x + 9 )
= - ( x² - 2.x.3 + 3² )
= - ( x - 3 )²
c) x² - 16
= x² - 4²
= ( x - 4 )( x + 4)
d) 9x² - 25
= ( 3x )² - 5²
= ( 3x - 5 )( 3x + 5 )
e ) x⁴ - y⁴
= ( x²)² - ( y² )²
= ( x² - y² )( x² + y² )
f) x⁶ -y⁶
= ( x³ )² - ( y³)^2
=( x³ - y³ )( x³ + y³ )

Answer 2

g) 8x³ - \(\dfrac{1}{27}\)
= ( 2x )³ - ( \(\dfrac{1}{3}\))³
= ( 2x - \(\dfrac{1}{3}\) ) ( 2x + \(\dfrac{2}{3}\)x + \(\dfrac{1}{3}\))

Answer 3

h) = ( 3x + \(\dfrac{1}{4}\)) . ( 9x² - \(\dfrac{3}{4}\)x + \(\dfrac{1}{16}\))

Answer 4

a) x² + 4x + 4 = x² + 2.2.x + 2² = ( x + 2 )²

b) 6x-9-x² = -x² + 6x - 9 = - ( x² - 6x + 9 ) = - ( x² - 2.x.3 +3² ) = - ( x-3)²

c) x² - 16 = ( x - 4 ) . ( x + 4 )

d) 9x² - 25 = ( 3x - 5 ) . ( 3x + 5 )

e) x⁴ -y⁴ = ( x² - y² ) .( x² + y² ) = ( x -y ) . ( x + y ) . ( x² + y² )

f) x⁶ - y⁶ = ( x³ - y³ ) . ( x³ + y³ )

g) 8x³ - \(\dfrac{1}{27}\) = ( 2x )³ - (\(\dfrac{1}{3}\))³ = ( 2x - \(\dfrac{1}{3}\)) . ( 4x² + \(\dfrac{2}{3}\)x + \(\dfrac{1}{9}\))

h) 27x³ + \(\dfrac{1}{64}\) = ( 3x )³ + (\(\dfrac{1}{4}\))³ = ( 3x + \(\dfrac{1}{4}\)) . ( 9x² - \(\dfrac{3}{4}\)x - \(\dfrac{1}{16}\))