Question

在实数范围内因式分解：(11)3x^2-4x-1(12)x^2-3x-9/4(13)2y^2-6y-3(14)-4a^2+6a+3(15)9y^2-6xy-x^2

(16)-2x^2+7xy-4y^2(17)4x^2-4xy-y^2(18)1/2x^4-5/2x^2+3(19)2x^3+3x^2-2x(20)y^4-9y^2+8(21)3x^4-6x^3+2x^2(22)3x^2-2x-2(23)2a^2-4ab-5b^2(24)-3x^2+4xy+10y^2(25)4x^2+12x+3<请写出详细过程>
<一共十五题>请写出详细过程。

Answer 1

(11)3x^2-4x-1
解：3x^2-4x-1
=3(x^2-4/3x-1/3)
令x^2-4/3x-1/3=0
解得：x=(2±√7)/3
即：3x^2-4x-1
=3(x^2-4/3x-1/3)
=3[x-(2+√7)/3][x-(2-√7)/3]
(12)x^2-3x-9/4
解：令x^2-3x-9/4=0
解得：x=(3±3√2)/2
即：x^2-3x-9/4
=[x-(3+3√2)/2][x-(3-3√2)/2]
(13)2y^2-6y-3
解：2y^2-6y-3
=2(y^2-3y-3/2)
令：y^2-3y-3/2=0
解得;y=(3±2√3)/2
即：2y^2-6y-3
=2(y^2-3y-3/2)
=2[y-(3+2√3)/2][y-(3-2√3)/2]
(14)-4a^2+6a+3
解：-4a^2+6a+3
= -4（a^2-3/2-3/4）
令a^2-3/2-3/4=0
解得：a=(3±√21)/4
即;-4a^2+6a+3
=-4[a-(3+√21)/4][a-(3-√21)/4]
(15)9y^2-6xy-x^2
解：9y^2-6xy-x^2
=9(y^2-2/3xy-1/9x^2)
令y^2-2/3xy-1/9x^2=0
解得：y=(3±3√2)/9 x
即：9y^2-6xy-x^2
=9(y^2-2/3xy-1/9x^2)
=9[y-(3+3√2)/9 x][y-(3-3√2)/9 x]
(16)-2x^2+7xy-4y^2
解：-2x^2+7xy-4y^2
=-2(x^2-7/2xy+2)
解得：x=(7±√17)/4 y
即：2x^2+7xy-4y^2
=-2(x^2-7/2xy+2)
= - 2[x-(7+√17)/4 y][x-(7-√17)/4 y]
(17)4x^2-4xy-y^2
解：4x^2-4xy-y^2
=4(x^2-xy-1/4y^2)
解得：x=(1±√2x)/2 y
4x^2-4xy-y^2
=4(x^2-xy-1/4y^2)
=4[x-(1+√2)/2 y][x-(1-√2)/2 y]
=[2x-(1+√2) y][2x-(1-√2) y]
(18)1/2x^4-5/2x^2+3
解：1/2x^4-5/2x^2+3
=1/2(x^4-5x^2+6)
=1/2(x-2)(x-3)
(19)2x^3+3x^2-2x
解：2x^3+3x^2-2x
=2x(x^2+3/2x-1)
=2x(x-1/2)(x+2)
(20)y^4-9y^2+8
解：y^4-9y^2+8
=(y^2-8)(y^2-1)
=(y-2√2)(y+2√2)(y-1)(y+1)
(21)3x^4-6x^3+2x^2
解：3x^4-6x^3+2x^2
=3x^2(x^2-2x+2/3)
令x^2-2x+2/3=0
解得：x=1±√3/3
即：3x^4-6x^3+2x^2
=3x^2(x^2-2x+2/3)
=3x^2[x-(1+√3/3)][x-(1-√3/3)]
(22)3x^2-2x-2
解：3x^2-2x-2
=3(x^2-2/3x-2/3)
令x^2-2/3x-2/3=0
解得：x=(1±√7)/3
即：3x^2-2x-2
=3(x^2-2/3x-2/3)
=3[x-(1+√7)/3][x-(1-√7)/3]
(23)2a^2-4ab-5b^2
解：2a^2-4ab-5b^2
=2(a^2-2ab-5/2b^2)
令a^2-2ab-5/2b^2=0 【把b看成常数】
解得：a=(2±√14)/2 b
即：2a^2-4ab-5b^2
=2(a^2-2ab-5/2b^2)
=2[x-(2-√14)/2 b][x-(2+√14)/2 b]
(24)-3x^2+4xy+10y^2
解：-3x^2+4xy+10y^2
=-3(x^2-4/3xy-10/3y^2) 【把y当做常数】
令x^2-4/3xy-10/3y^2=0
解得：x=(2±√34)/3 y
即:：-3x^2+4xy+10y^2
=-3(x^2-4/3xy-10/3y^2)
=-3[x-(2+√34)/3 y][x-(2-√34)/3 y]
(25)4x^2+12x+3
解：4x^2+12x+3
=4(x^2+3x+3/4)
令x^2+3x+3/4=0
解得:x=(-3±√6)/2
即：4x^2+12x+3
=4(x^2+3x+3/4)
=4[x-(-3+√6)/2][x-(-3-√6)/2]
=(2x+3-√6)(x+3+√6)