PTDTTNT: x(x+1)(x+2)(x+3)+1
Những câu hỏi liên quan
PTDTTNT
a) (x^2+x)^2+3(x^2+x)+2
b) (1+x^2)^2-4x(1-x^2)
PTDTTNT a , x^9 - x^7 - x^6 - x^5 +x^4 + x^3 + x^2 + 1
1.PTDTTNT
a)(2x+1)*(x+1)^2*(2x+3)-18
b) (x^2+4x+3)*(x^3+12x+35)+15
c0(x-3)*(x-5)*(x-6)*(x-10)-24x^2
a: \(\left(2x+1\right)\left(2x+3\right)\left(x+1\right)^2-18\)
\(=\left[\left(2x+2\right)^2-1\right]\left(x+1\right)^2-18\)
\(=4\left(x+1\right)^4-\left(x+1\right)^2-18\)
\(=4\left(x+1\right)^4-9\left(x+1\right)^2+8\left(x+1\right)^2-18\)
\(=\left(x+1\right)^2\left[4\left(x+1\right)^2-9\right]+2\left[4\left(x+1\right)^2-9\right]\)
\(=\left[\left(2x+2\right)^2-9\right]\left[\left(x+1\right)^2+2\right]\)
\(=\left(2x+5\right)\left(2x-1\right)\left(x^2+2x+3\right)\)
b: \(\left(x^2+4x+3\right)\left(x^2+12x+35\right)+15\)
\(=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+105+15\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+120\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
c: \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2\)
\(=\left(x^2-13x+30\right)\left(x^2-11x+30\right)-24x^2\)
\(=\left(x^2+30\right)^2-24x\left(x^2+30\right)+143x^2-24x^2\)
\(=\left(x^2+30\right)^2-24x\left(x^2+30\right)+119x^2\)
\(=\left(x^2-17x+30\right)\left(x^2-7x+30\right)\)
\(=\left(x-2\right)\left(x-15\right)\left(x^2-7x+30\right)\)
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PTDTTNT:
1. x^2-x-12
2. x^3-y^3-3x^2+3x-1
3. x^2-3xy+2y^2
4. 4X^3-5x^2-16x+20
a) x2 - x - 12
= x2 - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x - 4)(x + 3)
b) x3 - y3 - 3x2 + 3x - 1
= (x3 - 3x2 + 3x - 1) - y3
= (x - 1)3 - y3
= (x - 1 - y) [ (x - 1)2 + (x - 1)y + y2 ]
= (x - y - 1)(x2 - 2x + 1 + xy - y + y2 )
d) 4x3 - 5x2 - 16x + 20
= (4x3 - 8x2) + (3x2 - 6x) - (10x - 20)
= 4x2 (x - 2) + 3x(x - 2) - 10(x - 2)
= (x - 2)(4x2 + 3x - 10)
= (x - 2)(4x2 + 8x - 5x - 10)
= (x - 2)(x + 2)(4x - 5)
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Ptdttnt : A=(x+1)4+(x+3)4-2
PTDTTNT:
(x+1)4+(x2+x+1)
PTDTTNT
x^20+x+1
(x^2+y^2+1)^4-17(x^2+y^2+1)x^2+16x^4
PTDTTNT
x^20+x+1
(x^2+y^2+1)^4-17(x^2+y^2+1)x^2+16x^4
3. PTDTTNT
a) x^16 - 1
b) x^36 - 64
C) x^6 + y^6
d) a. ( x+5 ) . ( x+6 ) . ( x+10 ) . ( x+1 ) - 3x^2
Phân tích đa thức thành nhân tử:
a \(x^{16}-1\)
\(=\left(x^8\right)^2-1^2\)
\(=\left(x^8-1\right)\left(x^8+1\right)\)
b, \(x^{36}-64\)
\(=\left(x^{18}\right)^2-8^2\)
\(=\left(x^{18}-8\right)\left(x^{18}+8\right)\)
\(=\left[\left(x^6\right)^3-2^3\right]\left[\left(x^6\right)^3+2^3\right]\)
\(=\left(x-2\right)\left(x^{12}+2x+4\right)\left(x+2\right)\left(x^{12}-2x+4\right)\)
c, \(x^6+y^6\)
\(=\left(x^2\right)^3+\left(y^2\right)^3\)
\(=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)
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