a) \(4x^4+1\)
b) \(4x^4+81\)
c) \(64x^4+y^4\)
d) \(x^8+4\)
e) \(x^4+x^2+1\)
f) \(x^7+x^5+1\)
Những câu hỏi liên quan
phân tích các đa thức sau thành nhân tử:
1/(1+x^2)^2-4x(1-x^2)
2/(x^2-8)^2+36
3/x^4+4
4/x^4+64
5/64x^4+1
6/81x^4+4
7/4x^4+81
8/64x^4+y^4
9/x^4+4y^4
10/x^4+x^2+1
1: \(\left(x^2+1\right)^2-4x\left(1-x^2\right)\)
\(=x^4+2x^2+1-4x+4x^3\)
\(=x^4+4x^3+2x^2-4x+1\)
\(=\left(x^2+2x-1\right)^2\)
2: \(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+64+36\)
\(=x^4-16x^2+100\)
\(=x^4+20x^2+100-36x^2\)
\(=\left(x^2+10\right)^2-\left(6x\right)^2\)
\(=\left(x^2+6x+10\right)\left(x^2-6x+10\right)\)
3: \(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
4: \(x^4+64=x^4+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
5: \(64x^4+1=64x^4+16x^2+1-16x^2\)
\(=\left(8x^2+1\right)^2-16x^2\)
\(=\left(8x^2-4x+1\right)\left(8x^2+4x+1\right)\)
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Phân tích đa thức thành nhân tử
a) x^2+ 12x+35
b) x^2- x- 56
c) 5x^2- x-4
d) 4x^4+ 1
e) 4x^4+ 81
g) 64x^4+ y^4
a) \(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
b)\(x^2-x-56\)
\(=x^2+7x-8x-56\)
\(=\left(x^2+7x\right)-\left(8x+56\right)\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x+7\right)\left(x-8\right)\)
c)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
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TL:
a)\(x^2+5x+7x+35\)
=\(x\left(x+5\right)+7\left(x+5\right)\)
=\(\left(x+7\right)\left(x+5\right)\)
b) \(x^2-x-56\)
=\(x^2+7x-8x-56\)
=\(x\left(x+7\right)-8\left(x+7\right)\)
=\(\left(x-8\right)\left(x+7\right)\)
d)\(4x^4+1=\left(2x^2\right)^2+4x^2+1-4x^2\)
=\(\left(2x^2+1\right)^2-4x^2\)
=\(\left(2x^2+1+4x\right)\left(2x^2+1-4x\right)\)
.......................(tự lm)
hc tốt
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\(4\times^4+81\)
\(=\left(2\times^2\right)^2+36\times^2+9^2-36\times^2\)
\(=\left(2\times^2+9\right)^2-36\times^2\)
\(=\left(2\times^2+9+36\times\right)\left(2\times^2+9-36\times\right)\)
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Xem thêm câu trả lời
Câu 5: Phân tích đa thức thành nhân tử.
a) x2-7x+6. b)x4+64. c)x2+12x+35. d) 4x4+1
e)x2-x-56. f)4x4+81. g) 5x2-x-4. h)64x4+y4
a) x2-7x+6= (x-6)(x-1)
câu c,e , g tương tự nha bạn
b) x4+64= x4+16x2+64-16x2=(x2+8)2-16x2=(x2+8-4x)(x2+8+4x)
các câu còn lại cũng tượng tự nha bạn
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Câu 5: Phân tích đa thức thành nhân tử.
a) x2-7x+6. b)x4+64. c)x2+12x+35. d) 4x4+1
e)x2-x-56. f)4x4+81. g) 5x2-x-4. h) 64x4+y4
\(a,x^2-7x+6=x^2-6x-x+6\)
\(=x\left(x-6\right)-\left(x-6\right)=\left(x-1\right)\left(x-6\right)\)
\(b,x^4+64=\left(x^4+16x^2+64\right)-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
\(c,x^2+12x+35=x^2+5x+7x+35\)
\(=x\left(x+5\right)+7\left(x+5\right)=\left(x+7\right)\left(x+5\right)\)
\(d,4x^4+1=\left(4x^4+4x^2+1\right)-4x^2\)
\(=\left(2x^2+1\right)-\left(2x\right)^2=\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)\)
\(e,x^2-x-56=x^2-8x+7x-56\)
\(=x\left(x-8\right)+7\left(x-8\right)=\left(x+7\right)\left(x-8\right)\)
\(f,4x^2+81=\left(4x^4+36x^2+81\right)-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2=\left(2x^2+6x+9\right)\left(2x^2-6x+9\right)\)
\(g,5x^2-x-4=5x^2-5x+4x-4\)
\(=5x\left(x-1\right)+4\left(x-1\right)=\left(5x+4\right)\left(x-1\right)\)
\(h,64x^4+y^4=\left(64x^4+16x^2y^2+y^4\right)-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2+y^2+4xy\right)\left(8x^2+y^2-4xy\right)\)
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a) \(x^2-7x+6=x^2-6x-x+6\)
\(=x\left(x-6\right)-\left(x-6\right)\)
\(=\left(x-6\right)\left(x-1\right)\)
b) \(x^4+64=x^4+64+16x^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
c) \(x^2+12x+35=x^2+5x+7x+35\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
d) \(4x^4+1=4x^4+1+4x^2-4x^2\)
\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)
e) \(x^2-x-56=x^2+7x-8x-56\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x+7\right)\left(x-8\right)\)
f) \(4x^4+81=4x^4+81+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
g) \(5x^2-x-4=5x^2+4x-5x-4\)
\(=x\left(5x+4\right)-\left(5x+4\right)\)
\(=\left(5x+4\right)\left(x-1\right)\)
h) \(64x^4+y^4=64x^4+y^4+16x^2y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
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⚠ Cần gấp, Cần gấp ⚠
Bài 1: Phân tích đa thức thành nhân tử
a) x² - x - 56
b) x^4 + 64
c) 4x^4 + 81
d) x².+ 12x + 35
e) 5x² - x - 4
g) 4x^4 + 1
h) 64x^4 + y^4
Bài 2: Tìm x
a) x³ - 16x =0
b) x^4 - 2x³ + 10x² - 20x = 0
c) ( 2x - 1)² = ( x + 3 )²
d) x²( x - 2 ) - 2x² + 8x - 8 = 0
e) x^4 - 30x² + 31x - 30 = 0
Bài 1: Phân tích đa thức thành nhân tử
a) x² - x - 56
b) x^4 + 64
c) 4x^4 + 81
d) x².+ 12x + 35
e) 5x² - x - 4
g) 4x^4 + 1
h) 64x^4 + y^4
a) x² - x - 56
b) x^4 + 64
c) 4x^4 + 81
d) x².+ 12x + 35
e) 5x² - x - 4
g) 4x^4 + 1
h) 64x^4 + y^4
a)\(x^2-x-56\)
\(=x^2-8x+7x-56\)
\(=\left(x^2-8x\right)+\left(7x-56\right)\)
\(=x\left(x-8\right)+7\left(x-8\right)\)
\(=\left(x-8\right)\left(x+7\right)\)
b)\(x^4+64\)
\(=\left(x^2\right)^2+8^2\)
\(=\left(x^2\right)^2+16x^2+8^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
c)\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2\)
\(=\left(2x^2\right)^2+36x^2+9^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
d)\(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
e)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
g)\(4x^4+1\)
\(=\left(2x^2\right)^2+1^2\)
\(=\left(2x^2\right)^2+4x^2+1^2-4x^2\)
\(=\left(2x^2+1\right)^2-4x^2\)
\(=\left(2x^2+1-4x\right)\left(2x^2+1+4x\right)\)
h)\(64x^4+y^4\)
\(=\left(8x^2\right)^2+\left(y^2\right)^2\)
\(=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
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tìm x:
a, \(x^2-x-56\) b, \(4x^4+1\) c, \(5x^2-x-4\) d, \(4x^4+81\) e,\(64x^4+y^4\)
Làm nhanh giúp mk với
Mink nghĩ đề này là phân tích đa thức thành nhân tử chứ k phải tìm x^^
a) \(x^2-x-56=x^2-8x+7x-56=x\left(x-8\right)+7\left(x-8\right)=\left(x+7\right)\left(x-8\right)\)
b) \(4x^4+1=\left(4x^4+4x^2+1\right)-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)
c) \(5x^2-x-4=5x^2-5x+4x-4=5x\left(x-1\right)+4\left(x-1\right)=\left(x-1\right)\left(5x+4\right)\)
d) \(4x^4+81=\left(4x^4+36x^2+81\right)-36x^2=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9+6x\right)\left(2x^2+9-6x\right)\)
e) \(64x^4+y^4=\left(64x^4+16x^2y^2+y^4\right)-\left(4xy\right)^2=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
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a)\(x^2-x-56\)
\(=x^2+7x-8x-56\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x-8\right)\left(x+7\right)\)
b)\(4x^4+1\)
\(=\left(2x+1\right)^2-4x^2\)
\(=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
c)\(5x^2-x-4\)
\(=5x^2+4x-5x-4\)
\(=x\left(5x+4\right)-\left(5x+4\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
d)\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
e)\(64x^4+y^4\)
\(=\left(8x^2\right)^2+y^4+16x^2y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
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phân tích đa thức thành nhân tử :
a) 3(x^4+x^2+1)-(x^2+x+1)^2
b) 64x^4+y^4
c) x^3+3xy+y^3-1
d) 4x^4+4x^3+5x^2+2x+1
e) x^8+x+1
g) 3x^2+22xy+11x+37y
h) x^4-8x+63
1.Phân tích đa thức thành nhân tử:
a) a^4-4b^2
b) 9(a+b)^2-4(a-2b)^2
c)4(2a-b)^2-49(a-b)^2
d)4x^4+20x^2+25
e)9x^4+24x^2+16
f)4x^4-16x^2y^3+16y^6
g)9x^6-12x^7+4x^8
h)8x^6-27y^3
k)1/64x^6-125y^3
i)x^6+1
l)x^6-y^6
m)x^9+1
n)x^12-y^4
