Question

Answer 1

\(1.x^3-7x+6\\ =\left(x^3-x^2\right)+\left(x^2-x\right)+\left(-6x+6\right)\\ =x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x-6\right)\\ =\left(x-1\right)\left[x\left(x-2\right)+3\left(x-2\right)\right]\\ =\left(x-1\right)\left(x-2\right)\left(x+3\right)\\ 2.x^3-9x^2+6x+16\\ =\left(x^3+x^2\right)+\left(-10x^2-10x\right)+\left(16x+16\right)\\ =x^2\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\\ =\left(x^2-10x+16\right)\left(x+1\right)\\ =\left[x\left(x-2\right)-8\left(x-2\right)\right]\left(x+1\right)\\ =\left(x-2\right)\left(x-8\right)\left(x+1\right)\\ c.x^3-6x^2-x+30\\ =\left(x^3-5x^2\right)+\left(-x^2+5x\right)+\left(-6x+30\right)\\ =x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\\=\left(x-5\right)\left(x^2-x-6\right)\\ =\left(x-5\right)\left[x\left(x-3\right)+2\left(x-3\right)\right]\\ =\left(x-5\right)\left(x+2\right)\left(x-3\right)\\ d.2x^3-x^2+5x+3\\ =\left(2x^3+x^2\right)+\left(-2x^2-x\right)+\left(6x+3\right)\\ =x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\\ =\left(2x+1\right)\left(x^2-x+3\right)\)

Answer 2

các bn giúp mik lm hết giùm mik với

 

Answer 3

1) x^3 - 7x + 6
= x^3 - x^2 + x^2 - x - 6x + 6
= x^2(x - 1) + x(x - 1) - 6(x - 1)
= (x - 1)(x^2 + x - 6)
= (x - 1)(x^2 + 3x - 2x - 6)
= (x - 1)[x(x + 3) - 2(x + 3)]
= (x - 1)(x + 3)(x - 2)

2)${}^{}-9{}^{}+6x+16$

$={}^{}-8{}^{}-{}^{}+8x-2x+16$

$={}^{}\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)$

$=\left(x-8\right)\left({}^{}-x-2\right)$

$=\left(x-8\right)\left({}^{}-2x+x-2\right)$

Answer 4

Answer 5

1: \(x^3-7x+6\)

\(=x^3-x-6x+6\)

\(=x\left(x^2-1\right)-6\left(x-1\right)\)

\(=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x-6\right)=\left(x-1\right)\left(x+3\right)\left(x-2\right)\)

2: \(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)

\(=\left(x-8\right)\left(x^2-x-2\right)=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)

3: \(x^3-6x^2-x+30\)

\(=x^3-x^2-5x^2+5x-6x+30\)

\(=x^2\left(x-1\right)-5x\left(x-1\right)-6\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-5x-6\right)=\left(x-1\right)\left(x+1\right)\left(x-6\right)\)

4: \(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)=\left(2x+1\right)\left(x^2-x+3\right)\)

5: \(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)

6: \(x^2+2xy+y^2-x-y-12\)

\(=\left(x+y\right)^2-\left(x+y\right)-12\)

\(=\left(x+y-4\right)\left(x+y+3\right)\)

7: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

8: \(4x^4-32x^2+1\)

\(=4x^4+4x^2+1-36x^2\)

\(=\left(2x^2+1\right)^2-\left(6x\right)^2=\left(2x^2-6x+1\right)\left(2x^2+6x+1\right)\)

9: \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

\(=3\left(x^2+x+1\right)\left(x^2-x+1\right)-\left(x^2+x+1\right)^2\)

\(=\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\)

\(=\left(x^2+x+1\right)\left(2x^2-4x+2\right)=2\left(x-1\right)^2\cdot\left(x^2+x+1\right)\)

 

10: \(64x^4+y^4\)

\(=64x^4+16x^2y^2+y^4-16x^2y^2\)

\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)

\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)

11: \(a^6+a^4+a^2b^2+b^4-b^6\)

\(=\left(a^6-b^6\right)+\left(a^4+a^2b^2+b^4\right)\)

\(=\left(a^2-b^2\right)\left(a^4+a^2b^2+b^4\right)+\left(a^4+a^2b^2+b^4\right)\)

\(=\left(a^4+a^2b^2+b^4\right)\left(a^2-b^2+1\right)\)

12: \(x^3+3xy+y^3-1\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)+3xy-1\)

\(=\left[\left(x+y\right)^3-1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+\left(x+y\right)+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)

\(=\left(x+y-1\right)\left(x^2-xy+y^2+x+y+1\right)\)

13: \(4x^4+4x^3+5x^2+2x+1\)

\(=4x^4+2x^3+2x^2+2x^3+x^2+x+2x^2+x+1\)

\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)=\left(2x^2+x+1\right)^2\)

15: \(x^8+3x^4+4\)

\(=x^8+4x^4+4-x^4\)

\(=\left(x^4+2\right)^2-x^4\)

\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)

14: \(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)