实数范围内因式分解:(1) 3x^2-5x-4 (2) -2x^2+3x+1 (3) (x^2-8x)+5(x^2+8x
1个回答

配方后用平方差公式.

(1) 3x^2-5x-4

=3(X^2-5/3X-4/3)

=3[(X-5/6)^2-4/3-25/36]

=3[(X-5/6)^2-73/36]

=3(X-5/6+√73/6)(X-5/6-√73/6]

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

=-2(X^2-3/2X-1/2)

=-2[(X-3/4)^2-17/16]

=-2(X-3/4+√17/4)(X-3/4-√17/4)

(3) (x^2-8x)+5(x^2+8x)+6

=6X^2+32X+6

=6(X^2+16/3X+1)

=6[(X^2+8/3)^2+1-64/9]

=6[(X+8/3)^2-55/9]

=6(X+8/3+√55/3)(X-8/3-√55/3)