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a: \(=6x^3-12x^2+x^2-2x+x-2\)
\(=\left(x-2\right)\left(6x^2+x+1\right)\)
b: \(=3x^4+3x^3-x^3-x^2-7x^2-7x+5x+5\)
\(=\left(x+1\right)\left(3x^3-x^2-7x+5\right)\)
\(=\left(x+1\right)\left(3x^3-3x^2+2x^2-2x-5x+5\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(3x^2+2x-5\right)\)
\(=\left(x-1\right)^2\cdot\left(x+1\right)\left(3x+5\right)\)
c: \(=4x^3+x^2+4x^2+x+4x+1\)
\(=\left(4x+1\right)\left(x^2+x+1\right)\)
a) \(4x^4-27x^2y^2+y^4\)
\(=\left(2x^2\right)^2-2.2x^2.y^2+\left(y^2\right)^2-23x^2y^2\)
\(=\left(2x^2-y^2\right)^2-\left(\sqrt{23}xy\right)^2\)
\(=\left(2x^2-y^2-\sqrt{23}xy\right)\left(2x^2-y^2+\sqrt{23}xy\right)\)
b) Sửa đề \(x^3+5x^2+4x\)
\(=x^3+x^2+4x^2+4x\)
\(=x^2\left(x+1\right)+4x\left(x+1\right)\)
\(=x\left(x+1\right)\left(x+4\right)\)
c) Sửa đề \(x^3+5x^2+3x-9\)
\(=x^3-x^2+6x^2-6x+9x-9\)
\(=x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)\)
\(=\left(x-1\right)\left(x+3\right)^2\)
d) \(x^{16}+x^8-2\)
\(=x^{16}-x^8+2x^8-2\)
\(=x^8\left(x^8-1\right)+2\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+2\right)\)
Cho tam giác ABC vuông tại A có M là trung điểm BC. Vẽ MD vuông góc AC tại D.
a) Chứng minh ADMB là hình thang vuông
b) Lấy E thuộc tia MD,MD bằng DE. Chứng minh AMCE là hình bình hành
c) Gọi F là đối xứng của M qua BA. Chứng minh AF bằng AE
d) AB cắt MF tại Q. CQ cắt AM tại I. Chứng minh 3AD=BC,3AB=DE
1)x2-8x-9
= x^2 - 9x +x -9
= x(x+1) - 9 (x+1)
= (x-9) (x+1)
2)x2+3x-18
3)x3-5x2+4x
=x^3 - 4x^2 - x^2 + 4x
= x^2 (x-1) - 4x(x-1)
= (x^2 - 4x) (x-1)
= x(x-4)(x-1)
4)x3-11x2+30x
5)x3-7x-6
6)x16-64
\(=\left(x^8\right)^2-8^2\)
\(=\left(x^8-8\right)\left(x^8+8\right)\)
7)x3-5x2+8x-4
8)x2-3x+2
= x^2 - 2x - x +2
= x(x-1) -2(x-1)
= (x-2)(x-1)
1) \(\left(x-9\right)\left(x+1\right)\) 2) \(\left(x-3\right)\left(x+6\right)\) 3) \(x\left(x-4\right)\left(x-1\right)\)
4) \(x\left(x-6\right)\left(x-5\right)\) 5)\(\left(x-3\right)\left(x+1\right)\left(x+2\right)\) 6) ........
7) \(\left(x-1\right)\left(x-2\right)\left(x-2\right)\) 8) \(\left(x-2\right)\left(x-1\right)\)
a,A=x3+11x2+30x
A=x2(x+5)+6x2+30x
A=x2(x+5)+6x(x+5)
A=(x2+6x)(x+5)=x(x+5)(x+6)
e,( x+1)(x+3)(x+5)(x+7)+15
=(x2+8x+7)(x2+8x+15)+15
=(x2+8x+11-4)(x2+8x+11+4)+15
=(x2+8x+11)-1=(x2+8x+10)(x2+8x+12)
a) \(x^3-1+5x^2-5+3x-3\)
= \(x^3+5x^2+3x-9\)
= \(x^3-x^2+6x^2-6x+9x-9\)
= \(x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2+6x+9\right)\)
= \(\left(x-1\right)\left(x-3\right)^2\)
b) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
= \(\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]+1\)
= \(\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1\) (1)
Đặt \(x^2+5x+4=a\)
Đa thức (1) \(\Leftrightarrow a\left(a+2\right)+1\)
= \(a^2+2a+1=\left(a+1\right)^2=\left(x^2+5x+4+1\right)^2\)
= \(\left(x^2+5x+6\right)^2\)
c) \(x^8+x^4+1\)
Ta thấy \(\left\{{}\begin{matrix}x^8\ge0\\x^4\ge0\\1>0\end{matrix}\right.\) \(\Rightarrow x^8+x^4+1\ge1\)
\(\Rightarrow\) Không phân tích thành nhân tử đc.
d) \(x^3+x^2+4\)
= \(x^3+2x^2-x^2+4\)
= \(x^2\left(x-2\right)-\left(x^2-4\right)\)
= \(x^2\left(x-2\right)-\left(x-2\right)\left(x+2\right)\)
= \(\left(x-2\right)\left(x^2-x-2\right)\)
a) x3 - 1 + 5x2 - 5 + 3x - 3
= (x - 1)(x2 + x + 1) + 5(x - 1)(x + 1) + 3(x - 1)
= (x - 1)(x2 + x + 1 + 5x + 5 + 3)
= (x - 1)(x2 + 6x + 9)
= (x - 1)(x + 3)2
b) (x + 1)(x + 2)(x + 3)(x + 4) + 1
= (x2 + 4x + x + 4)(x2 + 3x + 2x + 6) + 1
= (x2 + 5x + 4)(x2 + 5x + 6) + 1 (1)
Đặt t = x2 + 5x + 5
=> x2 + 5x + 4 = t - 1
x2 + 5x + 6 = t + 1
(1) = (t - 1)(t + 1) + 1
= t2 - 1 + 1
= t2 = (x2 + 5x + 5)2
c) x8 + x4 + 1
= x8 + x7 + x6 - x7 - x6 - x5 + x5 + x4 + x3 - x3 - x2 - x + x2 + x + 1
= x6(x2 + x + 1) - x5(x2 + x + 1) + x3(x2 + x + 1) - x(x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)(x6 - x5 + x3 - x + 1)
a) \(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
b) \(5x^2-5xy-3x+3y\)
\(=5x\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-3\right)\)
c) \(x^2-2x-4y^2+1\)
\(=\left(x-1\right)^2-4y^2\)
\(=\left(x-2y-1\right)\left(x+2y-1\right)\)
c)\(x^4+4y^4=x^4+4x^2y^2+4y^4-4x^2y^2=\left(x^2+2y^2\right)^2-4x^2y^2=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
d)\(x^4+3x^2+4=x^4+4x^2+4-x^2=\left(x^2+2\right)^2-x^2=\left(x^2+2-x\right)\left(x^2+x+2\right)\)
c.
\(x^4+4y^4\)
\(=\left(x^2\right)^2+\left(2y^2\right)^2+4x^2y^2-4x^2y^2\)
\(=\left(x^2+2y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)