Question

分解因式：x(x+1)(x+2)(x+3)+1

Answer 1

(x²+3x)(x²+3x+2)+1
=(x²+3x)²+2(x²+3x)+1
=(x²+3x+1)²
有理分解就此打住
无理分解：
=(x²+3x+9/4-5/4)²
=((x+3/2)²-[（根号5）/2]²)²
=(x+(3-根号5)/2)²(x+(3+根号5)/2)²
此解法涵盖较为全面望采纳

Answer 2

原式=（x²+3x+2）（x²+3x）+1
令x²+3x为a
=a（a+2）+1
=a²+2a+1
=（x²+3x）²+2（x²+3x）+1
=x四次方+6x三次方+11X²+6x+1

Answer 3

x(x+1)(x+2)(x+3)+1
=[x(x+3)][(x+1)(x+2)]+1
=(x^2+3x)(x^2+3x+2)+1
设 x^2+3x =y
=y(y+2)+1
=y^2+2y+1
=(y+1)^2
=(x^2+3x+1)^2

Answer 4

x(x+1)(x+2)(x+3)+1
=x(x+3)(x+1)(x+2)+1
=(x*x+3x+1-1)(x*x+3x+1+1)+1
=(x*x+3x+1)^2 -1+1
=(x*x+3x+1)^2

Answer 5

x(x+1)(x+2)(x+3)+1
＝（x＾2＋3x）（x＾2＋3x＋2）＋1
＝（x＾2＋3x）＾2＋2（x＾2＋3x）＋1
＝（x＾2＋3x＋1）＾2