Question

Phân tích các đa thức sau thành nhân tử :
a, x^4 + x^3 + x + 1
b, x^4 - x^3 - x^2 + 1
c, ( 2x + 1 )^2 - ( x - 1 )^2
d, x^4 + 4x^2 - 5
Giúp mình với mình đang cần rất gấp ạ

Answer 1

a, x⁴ + x³ + x + 1

= x³(x + 1) + (x + 1)

= (x + 1)(x³ + 1)

= (x + 1)²(x² - x + 1)
b, x⁴ - x³ - x² + 1

= x³(x - 1) - (x - 1)(x + 1)

= (x - 1)(x³ - x - 1)
c, ( 2x + 1 )² - ( x - 1 )²

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

= 3x(x + 2)
d, x⁴ + 4x² - 5

= x⁴ - x² + 5x² - 5

= x²(x² - 1) + 5(x² - 1)

= (x² - 1)(x² + 5)

= (x - 1)(x + 1)(x² + 5)

Answer 2

a/ \(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)

b/ \(x^4-x^3-x^2+1=\left(x^4-x^3\right)-\left(x^2-1\right)=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left(x^3-x-1\right)\)

c/ \(\left(2x+1\right)^2-\left(x-1\right)^2=\left(2x+1-x+1\right)\left(2x+1+x-1\right)=3x\left(x+2\right)\)

d/ \(x^4+4x^2-5=x^4-x^2+5x^2-5=x^2\left(x^2-1\right)+5\left(x^2-1\right)=\left(x^2-1\right)\left(x^2+5\right)=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)