Phân tích đa thức thành nhân tử: x^3 + 3x^2 - 10x -24
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DH
0
TT
1
22 tháng 10 2016
a) \(-10x^2-17x+6\)
\(=-10x^2-20x+3x+6\)
\(=-10x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(3-10x\right)\)
b)\(x^2-10x+9\)
\(=x^2-x-9x+9\)
\(=x\left(x-1\right)-9\left(x-1\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
c) \(x^2-10x+24\)
\(=x^2-4x-6x+24\)
\(=x\left(x-4\right)-6\left(x-4\right)\)
\(=\left(x-4\right)\left(x-6\right)\)
10 tháng 9 2021
\(=-3\left(x^2-\dfrac{10}{3}x+\dfrac{5}{3}\right)\\ =-3\left(x^2-2\cdot\dfrac{5}{3}x+\dfrac{25}{9}-\dfrac{10}{9}\right)\\ =\dfrac{10}{3}-3\left(x-\dfrac{5}{3}\right)^2\\ =\left[\sqrt{\dfrac{10}{3}}-\sqrt{3}\left(x-\dfrac{5}{3}\right)\right]\left[\sqrt{\dfrac{10}{3}}+\sqrt{3}\left(x-\dfrac{5}{3}\right)\right]\\ =\left(\dfrac{\sqrt{30}}{3}+\dfrac{5\sqrt{3}}{3}-x\sqrt{3}\right)\left(\dfrac{\sqrt{30}}{3}-\dfrac{5\sqrt{3}}{3}+x\sqrt{3}\right)\)
\(=\left(\dfrac{\sqrt{30}+5\sqrt{3}}{3}-x\sqrt{3}\right)\left(\dfrac{\sqrt{30}+5\sqrt{3}}{3}-x\sqrt{3}\right)\)
10 tháng 9 2021
\(-3x^2+10x-5\)
\(=-3\left(x^2-\dfrac{10}{3}x+\dfrac{5}{3}\right)\)
\(=-3\left(x^2-2\cdot x\cdot\dfrac{5}{3}+\dfrac{25}{9}-\dfrac{10}{9}\right)\)
\(=-3\left(x-\dfrac{5+\sqrt{10}}{3}\right)\left(x-\dfrac{5-\sqrt{10}}{3}\right)\)
DD
1
16 tháng 2 2020
x^2 - 10x + 24
= x^2 - 4x - 6x + 24
= x(x - 4) - 6(x - 4)
= (x - 6)(x - 4)
VM
3
3 tháng 10 2021
a) \(x^2-3x=x\left(x-3\right)\)
b) \(10x\left(x-y\right)-8y\left(x-y\right)=2\left(x-y\right)\left(5x-4y\right)\)
c) \(x^2-9=\left(x-3\right)\left(x+3\right)\)
29 tháng 8 2021
\(g,x^4-16=\left(x^2-4\right)\left(x^2+4\right)=\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\\ i,-x^2+10x-25=-\left(x-5\right)^2\\ k,x^3+3x^2+3x+1-27z^3\\ =\left(x+1\right)^3-27z^3\\ =\left(x+1-3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\\ =\left(x-3z+1\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\\ m,\left(x+y\right)^2-25\left(x+y\right)+24=\left(x+y-5\right)^2-1=\left(x+y-4\right)\left(x+y-6\right)\)
KK
29 tháng 8 2021
g. x4 - 16
<=> x4 - 42
<=> (x2)2 - 42
<=> (x2 - 4)(x2 + 4)
i. -x2 + 10x - 25
<=> -(x2 - 10x + 25)
<=> -(x2 -10x + 52)
<=> -(x - 5)2
24 tháng 8 2023
a: =4x^2+8x-3x-6
=4x(x+2)-3(x+2)
=(x+2)(4x-3)
b: =3(3x^2-2x-1)
=3(3x^2-3x+x-1)
=3(x-1)(3x+1)
c: =2x^2-4x+x-2
=2x(x-2)+(x-2)
=(x-2)(2x+1)
d: =3x^2+3x-2x-2
=3x(x+1)-2(x+1)
=(x+1)(3x-2)
e: =3x^2+9x+x+3
=3x(x+3)+(x+3)
=(x+3)(3x+1)
24 tháng 8 2023
a) \(4x^2+5x-6\)
\(=4x^2+8x-3x-6\)
\(=\left(4x^2+8x\right)-\left(3x+6\right)\)
\(=4x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(4x-3\right)\)
b) \(9x^2-6x-3\)
\(=3\left(3x^2-2x-1\right)\)
\(=3\left(3x^2-3x+x-1\right)\)
\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)
\(=3\left(x-1\right)\left(3x+1\right)\)
c) \(2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=\left(2x^2-4x\right)+\left(x-2\right)\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
d) \(3x^2+x-2\)
\(=3x^2+3x-2x-2\)
\(=\left(3x^2+3x\right)-\left(2x+2\right)\)
\(=3x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-2\right)\)
e) \(3x^2+10x+3\)
\(=3x^2+9x+x+3\)
\(=3x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(3x+1\right)\)
\(=x^3-3x^2+6x^2-18x+8x-24\\ =\left(x-3\right)\left(x^2+6x+8\right)\\ =\left(x-3\right)\left(x^2+2x+4x+8\right)\\ =\left(x-3\right)\left(x+2\right)\left(x+4\right)\)
\(x^3+3x^2-10x-24=\left(x^3-3x^2\right)+\left(6x^2-18x\right)+\left(8x-24\right)=x^2\left(x-3\right)+6x\left(x-3\right)+8\left(x-3\right)=\left(x-3\right)\left(x^2+6x+8\right)=\left(x-3\right)\left[\left(x^2+2x\right)+\left(4x+8\right)\right]=\left(x-3\right)\left[x\left(x+2\right)+4\left(x+2\right)\right]=\left(x-3\right)\left(x+2\right)\left(x+4\right)\)