Question

phân tích đa thức thành nhân tử

a) x³ +3x² - 4xy² - 12y³

^b) x³ + 4y² - 2xy + x² + 8y³

^c) 2x² + 9x - 5

d) 3x² - 10x - 8

e) x⁵ + x⁴ +1

 

Answer 1

a) Ta có : x³ + 3x² - 4xy² - 12y³

= x²(x + 3) - 4y²(x + 3)

= (x + 3)(x² - 4y²)

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

Answer 2

e) x⁵ + x⁴ + 1 

= x⁵ + x⁴ + x³ - x³ - x² - x + x² + x + 1 

= ( x⁵ + x⁴ + x³) - (x³ + x² + x) + ( x² + x + 1)

= x³(x² + x + 1) - x(x² + x + 1) + (x² + x + 1 )

= (x² + x + 1 )(x³ - x + 1)

Answer 3

b)\(x^3+4y^2-2xy+x^{^2}+8y^3=\left(x^3+8y^3\right)+\left(4y^2-2xy+x^2\right)=\)\(\left(x+2y\right)\left(x^2-2xy+4y^2\right)+1\left(4y^2-2xy+x^2\right)\)=\(\left(x+2y+1\right)\left(x^2-2xy+4y^2\right)\)

Answer 4

a) Sai

Answer 5

\(c,2x^2+9x-5\)

\(=2x^2+10x-x-5\)

\(=2x\left(x+5\right)-\left(x+5\right)\)

\(=\left(2x-1\right)\left(x+5\right)\)

\(d,3x^2-10x-8\)

\(=3x^2-12x+2x-8\)

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

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