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b) 3x4-3x3+9x3-9x2-24x2+24x-48x+48
=3x3(x-1)+9x2(x-1)-24x(x-1)-48(x-1)
=(x-1)(3x3+9x2-24x-48)
=3(x-1)(x3+3x2-8x-16)
a) \(x^2-2x-15\)
\(\Leftrightarrow x^2-2x+1-16\)
\(\Leftrightarrow\left(x-1\right)^2-4^2\)
\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\)
\(a,x^2-2x-15=\left(x^2-2x+1\right)-16.\)
\(=\left(x-1\right)^2-4^2\)
\(=\left(x-5\right)\left(x+3\right)\)
3: \(15x^3+29x^2-8x-12\)
\(=15x^3+30x^2-x^2-2x-6x-12\)
\(=\left(x+2\right)\left(15x^2-x-6\right)\)
\(=\left(x+2\right)\left(15x^2-10x+9x-6\right)\)
\(=\left(x+2\right)\left(3x-2\right)\left(3x+5\right)\)
5: \(x^3+9x^2+26x+24\)
\(=x^3+4x^2+5x^2+20x+6x+24\)
\(=\left(x+4\right)\left(x^2+5x+6\right)\)
\(=\left(x+4\right)\left(x+2\right)\left(x+3\right)\)
/ (4x−2)(10x+4)(5x+7)(2x+1)+17=0(4x−2)(10x+4)(5x+7)(2x+1)+17=0
⇔(4x−2)(5x+7)(10x+4)(2x+1)+17=0⇔(4x−2)(5x+7)(10x+4)(2x+1)+17=0
⇔(20x2+18x−14)(20x2+18x+4)+17=0⇔(20x2+18x−14)(20x2+18x+4)+17=0
Đặt t= 20x2+18x+4(t≥0)20x2+18x+4(t≥0) ta có:
(t-18).t +17=0
⇔t2−18t+17=0⇔t2−18t+17=0
⇔(t−17)(t−1)=0⇔(t−17)(t−1)=0
⇔[t=17(tm)t=1(tm)⇔[t=17(tm)t=1(tm) ⇔[20x2+18x+4=1720x2+18x+4=1⇔[20x2+18x−13=020x2+18+3=0⇔[20x2+18x+4=1720x2+18x+4=1⇔[20x2+18x−13=020x2+18+3=0
⇔[(20x+9−341−−−√)(20x+9+341−−−√)=0(20x+9−21−−√)(20x+9+21−−√)=0⇔[(20x+9−341)(20x+9+341)=0(20x+9−21)(20x+9+21)=0
⇔⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢x=−9+341−−−√20x=−9−341−−−√20x=−9+21−−√20x=−9−21−−√20
\(a,\)\(\left(4x-2\right)\left(10x+4\right)\left(5x+7\right)\left(2x+1\right)+17\)
\(=\left(4x-2\right)\left(5x+7\right)\left(10x+4\right)\left(2x+1\right)+17\)
\(=\left(20x^2+18x-5\right)\left(20x^2+18x+4\right)+17\)
Đặt ....
b mk thấy nó sai đề sao ý
c) \(C=\left(x^2+x+4\right)^2+8x\left(x^2+x+4\right)+15x^2\)
\(=\left(x^2+x+4\right)^2+2.4x.\left(x^2+x+4\right)+16x^2-x^2\)
\(=\left(x^2+x+4+4x\right)^2-x^2\)
\(=\left(x^2+5x+4\right)^2-x^2\)
\(=\left(x^2+5x+4-x\right)\left(x^2+5x+4+x\right)=\left(x^2+4x+4\right)\left(x^2+6x+4\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) x4 - 10x3 - 15x2 + 20x + 4
= x4 + 2x3 - 12x3 - 24x2 + 9x2 + 18x + 2x + 4
= x3(x + 2) - 12x2(x + 2) + 9x(x + 2) + 2(x + 2)
= (x + 2)(x3 - 12x2 + 9x + 2)
b)
2x4 - 5x3 - 27x2 + 25x + 50
= 2x3(x - 2) - x2(x - 2) - 25x(x - 2) - 25(x - 2)
= (x - 2)(2x3 - x2 - 25x - 25)
c)\(3x^4+6x^3-33x^2-24x+48\)
\(=3\left(x^4+2x^3-11x^2-8x+16\right)\)
\(=3\left(x^4-x^3-4x^2+3x^3-3x^2-12x-4x^2+4x+16\right)\)
\(=3\left(x^2\left(x^2-x-4\right)+3x\left(x^2-x-4\right)-4\left(x^2-x-4\right)\right)\)
\(=3\left(x^2+3x-4\right)\left(x^2-x-4\right)\)
\(=3\left(x^2-x+4x-4\right)\left(x^2-x-4\right)\)
\(=3\left[x\left(x-1\right)+4\left(x-1\right)\right]\left(x^2-x-4\right)\)
\(=3\left(x-1\right)\left(x+4\right)\left(x^2-x-4\right)\)