phân tích đa thức thành nhân tử:
\(x^3 +6x^2-13x-42\)
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BT
3
1 tháng 8 2016
\(x^3+6x^2-13x-42\)
\(x^3+6x^2-13x-42\)
\(=\left(x+7\right)\left(x-3\right)\left(x+2\right)\)
2 tháng 8 2016
b, \(2x^3-x^2+3x+6\)
\(=2x^3+2x^2-3x^2-3x+6x+6\)
\(=2x^2\left(x+1\right)-3x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^2-3x+6\right)\)
NS
1
29 tháng 10 2021
\(P\left(x\right)=6x^3+13x^2+4x-3\)
\(=\left(6x^3+6x^2\right)+\left(7x^2+7x\right)-\left(3x-3\right)\)
\(=6x^2\left(x+1\right)+7x\left(x+1\right)-3\left(x+1\right)\)
\(=\left(6x^2+7x-3\right)\left(x+1\right)\)
\(=\left[\left(6x^2-2x\right)+\left(9x-3\right)\right]\left(x+1\right)\)
\(=\left[2x\left(3x-1\right)+3\left(3x-1\right)\right]\left(x+1\right)\)
\(=\left(3x-1\right)\left(2x+3\right)\left(x+1\right)\)
30 tháng 9 2021
e) \(=x^2\left(x+1\right)-2x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x^2-2x+3\right)\)
g) \(=x^2\left(3x-1\right)-x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(x^2-x+4\right)\)
h) \(=3x^2\left(2x+1\right)-x\left(2x+1\right)+\left(2x+1\right)=\left(2x+1\right)\left(3x^2-x+1\right)\)
i) \(=2x^2\left(2x+1\right)+2x\left(2x+1\right)+\left(2x+1\right)=\left(2x+1\right)\left(2x^2+2x+1\right)\)
T
2
17 tháng 10 2021
\(=6x^2+3x+10x+5=3x\left(2x+1\right)+5\left(2x+1\right)=\left(3x+5\right)\left(2x+1\right)\)
8 tháng 7 2016
=6x^2 - 4x - 9x +6
=(6x^2 -4x) - (9x-6)
=2x(3x -2) - 3(3x-2)
=(3x-2) (2x - 3)
TM
20 tháng 11 2016
a) \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left[\left(x+8\right)-\left(x-2\right)\right]^2\)
\(=\left(x+8-x+2\right)^2\)
\(=10^2\)
\(=2^2.5^2\)
b)\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
c)\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
d)\(x^3+6x^2-13x-42=x^3-3x^2+9x^2-27x+14x-42\)
\(=x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+9x+14\right)\)
\(=\left(x-3\right)\left(x^2+2x+7x+14\right)\)
\(=\left(x-3\right)\left[x\left(x+2\right)+7\left(x+2\right)\right]\)
\(=\left(x-3\right)\left(x+2\right)\left(x+7\right)\)
CN
1
KT
1 tháng 2 2018
\(x^4+6x^3+13x^2+12x+4\)
\(=x^4+x^3+5x^3+5x^2+8x^2+8x+4x+4\)
\(=x^3\left(x+1\right)+5x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+5x^2+8x+4\right)\)
\(=\left(x+1\right)\left(x^3+x^2+4x^2+4x+4x+4\right)\)
\(=\left(x+1\right)\left[x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\right]\)
\(=\left(x+1\right)^2\left(x+2\right)^2\)
M
18 tháng 8 2018
\(6x^2+13x-15\)
\(=6x^2+18x-5x-15\)
\(=6x.\left(x+3\right)-5.\left(x+3\right)\)
\(=\left(x+3\right).\left(6x-5\right)\)
18 tháng 8 2018
\(6x^2+13x-15\)
\(=6x^2+18x-5x-15\)
\(=6x\left(x+3\right)-5\left(x+3\right)\)
\(=\left(x+3\right)\left(6x-5\right)\)
HT
3
29 tháng 9 2019
a) Ta có : 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
b) Ta có: 6x2 + 7x - 3 = 6x2 + 9x - 2x - 3 = 3x(2x + 3) - (2x + 3) = (3x - 1)(2x + 3)
BA
29 tháng 9 2019
\(a,6x^2-13x+6\)
\(=6x^2-9x-4x+6\)
\(=3x\cdot\left(2x-3\right)-x\cdot\left(2x-3\right)\)
\(=\left(2x-3\right)\cdot\left(3x-x\right)\)
\(=\left(2x-3\right)\cdot2x\)
\(b,6x^2+7x-3\)
\(=6x^2-2x+9x-3\)
\(=2x\cdot\left(3x-1\right)+3\cdot\left(3x-1\right)\)
\(=\left(3x-1\right)\cdot\left(2x+3\right)\)
\(x^3+6x^2-13x-42\)
\(=x^3-3x^2+9x^2-27x+14x-42\)
\(=x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+9x+14\right)\)
\(=\left(x-3\right)\left(x^2+7x+2x+14\right)\)
\(=\left(x-3\right)\left(x+7\right)\left(x+2\right)\)
Chúc bạn học tốt!!!
thank bạn!