1/ Phân tích đa thức thành nhân tử:
a/x^3 + 4x^2 - 29x +24
b/x^4 +6x^3 +7x^2 - 6x +1
c/(x^2 -x +2)^2 + (x-2)^2
d/6x^5 + 15x^4 + 20x^3 + 15x^2 + 6x +1
e/x^6 + 3x^5 + 4x^4 + 4x^3 + 4x^2 + 3x +1
B1: phân tích đa thức
a)\(x^3+4x^2-29x+24\)
b)\(x^4+6x^3+7x^2+6x+1\)
c)\(\left(x^2-x+2\right)^2+\left(x-2\right)^2\)
d)\(6x^5+15x^4+20x^3+15x^2+6x+1\)
e)\(x^6+3x^5+4x^4+4x^3+4x^2+3x+1\)
B2:phân tích đa thức
a)\(x^8+x^4+1\)
b)\(x^{10}+x^5+1\)
c)\(x^{12}+1\)
B3: phân tích đa thức
a)\(\left(x+y+z\right)^3-x^3-y^3-z^3\)
b)\(\left(x+y+z\right)^5-x^5-y^5-z^5\)
AI LÀM ĐC PHẦN NÀO THÌ LÀM KO CẦN LÀM HẾT GIÚP MK MAI NỘP BÀI RỒI
\(x^8+x^4+1\)
\(=\left(x^8+2x^4+1\right)-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)
\(=\left(x^4-x^2+1\right)\left(x^4+2x^2-x^2+1\right)\)
\(=\left(x^4-x^2+1\right)[\left(x^2+1\right)^2-x^2]\)
\(=\left(x^4-x^2+1\right)\left(x^2+1-x\right)\left(x^2+1+x\right)\)
Phân tích đa thức thành nhân tử
1. \(15x^3+29x^2-8x-12\)
2.\(x^3+4x^2-29x+24\)
3.\(x^4+6x^3+7x^2-6x+1\)
4.\(x^3+4x^2-31x-70\)
5.\(5x^4+24x^3-15x^2-118x+24\)
6.\(x^4-6x^3+7x^2+6x-8\)
1)
\(15x^3+29x^2-8x-12=(15x^3+30x^2)-(x^2+2x)-(6x+12)\)
\(=15x^2(x+2)-x(x+2)-6(x+2)\)
\(=(x+2)(15x^2-x-6)=(x+2)(15x^2-10x+9x-6)\)
\(=(x+2)[5x(3x-2)+3(3x-2)]\)
\(=(x+2)(3x-2)(5x+3)\)
2)
\(x^3+4x^2-29x+24=(x^3-x^2)+(5x^2-5x)-(24x-24)\)
\(=x^2(x-1)+5x(x-1)-24(x-1)\)
\(=(x-1)(x^2+5x-24)\)
\(=(x-1)(x^2-3x+8x-24)\)
\(=(x-1)[x(x-3)+8(x-3)]=(x-1)(x-3)(x+8)\)
3.
\(x^4+6x^3+7x^2-6x+1\)
\(=(x^4+6x^3+9x^2)-2x^2-6x+1\)
\(=(x^2+3x)^2-2x^2-6x+1\)
\(=(x^2+3x)^2-2(x^2+3x)+1=(x^2+3x-1)^2\)
4.
\(x^3+4x^2-31x-70=(x^3+2x^2)+(2x^2+4x)-(35x+70)\)
\(=x^2(x+2)+2x(x+2)-35(x+2)\)
\(=(x+2)(x^2+2x-35)\)
\(=(x+2)(x^2-5x+7x-35)\)
\(=(x+2)[x(x-5)+7(x-5)]\)
\(=(x+2)(x-5)(x+7)\)
1) Phân tích đa thức thành nhân tử ( = cách nhẩm nghiệm và hệ số bất định)
a) x^4+6x^3+11x^2+6x+1
b)x^4+7x^3+14x^2+14x+4
c)x^4-1ox^3-15x^2+20x+4
2)phân tích đa thức thành nhân tử( = cách hệ số bất định)
a) x^4-8x^3+11x^2+8x+12
b) x^4+x^2+1
c)x^4+4
1.PTĐT thành nhân tử
a) \(x^5+4x+5\)
b) \(x^4+6x^3+11x^2+6x+1\)
c) \(64x^4+1\)
c) \(81x^4+4\)
d) \(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)-3x^2\)
e) \(x^5-x^4-1\)
2.PTĐT thành nhân tử (PP hệ số bất định)
a) \(3x^2-22xy-4x+8y+7y^2+1=\left(3x+ay+b\right)\left(x+cy+d\right)\)
b) \(12x^2+5x-12y^2+12y-10xy-3=\left(ã+by-1\right)\left(dx+cy+3\right)\)
a) \(x^5+4x+5=\left(x^5+x^4\right)-\left(x^4+x^3\right)+\left(x^3+x^2\right)-\left(x^2+x\right)+\left(5x+5\right)=x^4\left(x+1\right)-x^3\left(x+1\right)+x^2\left(x+1\right)-x\left(x+1\right)+5\left(x+1\right)=\left(x^4-x^3+x^2-x+5\right)\left(x+1\right)\)
b) \(x^4+6x^3+11x^2+6x+1=\left(x^4+3x^3+x^2\right)+\left(3x^3+9x^2+3x\right)+\left(x^2+3x+1\right)=x^2\left(x^2+3x+1\right)+3x\left(x^2+3x+1\right)+\left(x^2+3x+1\right)=\left(x^2+3x+1\right)^2\)
c) \(64x^4+1=\left[\left(8x^2\right)^2+16x^2+1\right]-16x^2=\left(8x^2+1\right)^2-\left(4x\right)^2=\left(8x^2-4x+1\right)\left(8x^2+4x+1\right)\)d) \(81x^4+4=\left[\left(9x^2\right)^2+36x^2+2^2\right]-36x^2=\left(9x^2+2\right)^2-\left(6x\right)^2=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)
Câu 1:
\(e,x^5-x^4-1=x^5-x^4+x^3-x^3+x^2-x^2+x-x-1\\ =\left(x^5-x^4-x^3\right)+\left(x^3-x^2-x\right)+\left(x^2-x-1\right)\\ =x^3\left(x^2-x-1\right)+x\left(x^2-x-1\right)+\left(x^2-x-1\right)\\ =\left(x^2-x-1\right)\left(x^3+x+1\right)\)
Câu 2:
\(a,\left(3x+ay+b\right)\left(x+cy+d\right)\\ =3x^2+3xcy+3xd+axy+acy^2+ayd+bx+bcy+bd\\ =3x^2+xy\left(3c+a\right)+x\left(b+3d\right)+y\left(ad+bc\right)+acy^2+bd\\ \Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}3c+a=-22\\b+3d=-4\end{matrix}\right.\\ad+bc=8\\\left\{{}\begin{matrix}ac=7\\bd=1\end{matrix}\right.\end{matrix}\right.\)
Xét \(bd=1\Leftrightarrow\left[{}\begin{matrix}b=1;d=1\\b=-1;d=-1\end{matrix}\right.\)
Với \(b=1;d=1\Leftrightarrow b+3d=1+3\cdot1=4\left(ktm\right)\)
Với \(b=-1;d=-1\Leftrightarrow b+3d=-1-3=-4\left(tm\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}3c+a=-22\\-a-c=8\\ac=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-1\\c=-7\end{matrix}\right.\)
Vậy \(3x^2-22xy-4x+8y+7y^2+1=\left(3x-y-1\right)\left(x-7y-1\right)\)
Cái chỗ ngoặc nhọn mà 5 dòng á a ko thấy trong cái phần công thức nên là ghi z chứ nó có 5 dòng đó nha
câu b tương tự, lười wa 😴
1. Phân tích đa thức thành nhân tử: a) (x+4)^2+8x(x+4)^3+15x^2
2. Tìm x: a) 3x(x-2020)-x+2020=0
b)(2x-3).(3x+2)-6x^2=1
c)(3x-1)^2-(x+5)^2=0
d)4x^2-4x-35=0
Phân tích đa thức thành nhân tử:
a) \(x^3+4x^2-29x+24\)
b) \(x^4+6x^3+7x^2-6x+1\)
a) nhận xét hệ số : 1 + 4 - 29 + 24 = 0
=> x3 + 4x2 - 29x + 24 = x2(x-1) + 5x(x-1) - 24(x-1)
= (x-1)(x2+5x-24) = (x-1)(x-3)(x+8)
b) ...
a) \(x^3+4x^2-29x+24\)=\(\left(x+8\right)\left(x^2-4x+3\right)\)=\(\left(x+8\right)\left(x^2-x-3x+3\right)\)=\(\left(x+8\right)\left(x-1\right)\left(x-3\right)\)
b) \(x^4+6x^3+7x^2-6x+1\)=\(x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)=\(x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)^2\)
Phân tích đa thức thành nhân tử:
1. 4x^2 - 4x – 3
2. 2x^2 - 5x - 3
3. 3x^2 - 5x - 2
4. 2x^2 + 5x + 2
5. 6x^2 - x - 1
6. 6x^2 - 6x - 3
7. 15x^2 - 2x - 1
8. x^4 – 13x^2 + 36
\(1.\)
\(4x^2-4x-3\)
\(=4x^2-2x+6x-3\)
\(=2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
\(2.\)
\(2x^2-5x-3\)
\(=2x^2-6x+x-3\)
\(=2x\left(x-3\right)+\left(x-3\right)\)
\(=\left(2x+1\right)\left(x-3\right)\)
\(3.\)
\(3x^2-5x-2\)
\(=3x^2+x-6x-2\)
\(=x\left(3x+1\right)-2\left(3x+1\right)\)
\(=\left(3x+1\right)\left(x-2\right)\)
\(4.\)
\(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+\left(x+2\right)\)
\(=\left(2x+1\right)\left(x+2\right)\)
\(5.\)
\(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=2x\left(3x+1\right)-\left(3x+1\right)\)
\(=\left(2x-1\right)\left(3x+1\right)\)
\(6.\)
\(6x^2-6x-3\)
\(=3\left(2x^2-2x-1\right)\)
\(7.\)
\(15x^2-2x-1\)
\(=15x^2+3x-5x-1\)
\(=3x\left(5x+1\right)-1\left(5x+1\right)\)
\(=\left(5x+1\right)\left(3x-1\right)\)
\(8.\)
\(x^4-13x^2+36\)
\(=\left(x-3\right)\left(x^3+3x^2-4x-12\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x^2+5x+6\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)\)
phân tích đa thức thành nhân tử:
a)2x^3-3x^2+3x-1
b)x^4-6x^3+12x^2-14x+3
c)3x^2-22xy-4x-8y+7y^2+1
d)x(x+1)(x+2)(x+3)+1
e)(x+2)(x+3)(x+4)(x+5)-24
g)x^4-8x+6;f)6x^4-11x^2+3
Phân tích đa thức thành nhân tử:
1, x^3-x+y^3-4
2, 4x^2-y^2+4x+1
3, x^4+2x^3+x^2
4, x^2+5x-6
5, 7x-6x^2-2
6, 5x^2+5xy-x-y
7, 2x^2+3x-5
8,x^4-5x^2+4
9, x^3-5x^2+45-9x
10, x^4-2x^3-2x^2-2x-3
11, 81x^4+4
12,x^5+x+1
13, x^4+6x^3+7x^2-6x+1
14, x(x+4)(x+6)(x+10)+128
2: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
3: =x^2(x^2+2x+1)
=x^2(x+1)^2
4: =x^2+6x-x-6
=(x+6)(x-1)
5: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
6: =5x(x+y)-(x+y)
=(x+y)(5x-1)
7: =2x^2+5x-2x-5
=(2x+5)(x-1)
8: =(x^2-1)*(x^2-4)
=(x-1)(x+1)(x-2)(x+2)
9: =x^2(x-5)-9(x-5)
=(x-5)(x-3)(x+3)