Phân tích đa thức thành nhân tử
1, 4x^2 - 13x + 9
2, 5x^2 + 17x + 12
3, x^2 - 3x - 10
4, x^2 + x - 12
5, x^3 + 5x^2 + 3x - 9
6, x^3 - 7x + 6
7, x^5 - 5x^3 + 4x
8, 4x^4 - 21x^2y^2 + y^4
9, 2a^2b + 4ab^2 - a^2c + ac^2 - 4b^2c + 2bc^2 - 4abc
10, 8x^3(y+z) - y^3(z+2x) - z^3(2x-y)
1. $4x^2-13x+9$
$=4x^2-4x-9x+9$
$=4x(x-1)-9(x-1)$
$=(x-1)(4x-9)$
2. $5x^2+17x+12$
$=5x^2+5x+12x+12$
$=5x(x+1)+12(x+1)$
$=(x+1)(5x+12)$
3. $x^2-3x-10$
$=x^2+2x-5x-10$
$=x(x+2)-5(x+2)$
$=(x+2)(x-5)$
4. $x^2+x-12$
$=x^2-3x+4x-12$
$=x(x-3)+4(x-3)$
$=(x-3)(x+4)$
5. $x^3 + 5x^2 + 3x - 9$
$=x^3-x^2+6x^2-6x+9x-9$
$=x^2(x-1)+6x(x-1)+9(x-1)$
$=(x-1)(x^2+6x+9)$
$=(x-1)(x+3)^2$
6. $x^3 - 7x + 6$
$=x^3-1-7x+7$
$=(x-1)(x^2+x+1)-7(x-1)$
$=(x-1)(x^2+x+1-7)$
$=(x-1)(x^2-2x+3x-6)$
$=(x-1)[x(x-2)+3(x-2)]$
$=(x-1)(x-2)(x+3)$
7. $x^5 - 5x^3 + 4x$
$=x(x^4-5x^2+4)$
$=x(x^4-x^2-4x^2+4)$
$=x[x^2(x^2-1)-4(x^2-1)$
$=x(x^2-1)(x^2-4)$
$=x(x-1)(x+1)(x-2)(x+2)$
8. $4x^4 - 21x^2y^2 + y^4$
$=(4x^4+4x^2y^2+y^4)-25x^2y^2$
$=(2x^2+y^2)^2-25x^2y^2$
$=(2x^2+y^2-5xy)(2x^2+y^2+5xy)$
9. $2a^2b + 4ab^2 - a^2c + ac^2 - 4b^2c + 2bc^2 - 4abc$
$=(2a^2b-2abc)+(4ab^2-4b^2c)-(a^2c-ac^2)-(2abc-2bc^2)$
$=2ab(a-c)+4b^2(a-c)-ac(a-c)-2bc(a-c)$
$=(a-c)(2ab+4b^2-ac-2bc)$
$=(a-c)[2b(a+2b)-c(a+2b)]$
$=(a-c)(a+2b)(2b-c)$
10. $8x^3(y+z) - y^3(z+2x) - z^3(2x-y)$
$=8x^3(y+z)-y^3z-2xy^3-2xz^3+yz^3$
$=8x^3(y+z)-(y^3z-yz^3)-(2xy^3+2xz^3)$
$=8x^3(y+z)-yz(y-z)(y+z)-2x(y+z)(y^2-yz+z^2)$
$=(y+z)[8x^3-yz(y-z)-2x(y^2-yz+z^2)]$
$=(y+z)(8x^3-y^2z+yz^2-2xy^2+2xyz-2xz^2)$
$=(y+z)[(8x^3-2xy^2)+(2xyz-y^2z)-(2xz^2-yz^2)]$
$=(y+z)[2x(2x+y)(2x-y)+yz(2x-y)-z^2(2x-y)]$
$=(y+z)(2x-y)(4x^2+2xy+yz-z^2)$
$=(y+z)(2x-y)[(2x+z)(2x-z)+y(2x+z)]$
$=(y+z)(2x-y)(2x+z)(2x+y-z)$
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
