\(x^2+9x+20\)

\(\Leftrightarrow x^2+4x+5x+20\)

\(\Leftrightarrow\left(x^2+4x\right)+\left(5x+20\right)\)

\(\Leftrightarrow x\left(x+4\right)+5\left(x+4\right)\)

\(\Leftrightarrow\left(x+4\right)\left(x+5\right)\)

\(x^2-x-20\)

\(\Leftrightarrow x^2-5x+4x-20\)

\(\Leftrightarrow\left(x^2-5x\right)+\left(4x-20\right)\)

\(\Leftrightarrow x\left(x-5\right)+4\left(x-5\right)\)

\(\Leftrightarrow\left(x-5\right)\left(x+4\right)\)

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

\(\Leftrightarrow3x^2+3x-2x-2\)

\(\Leftrightarrow\left(3x^2+3x\right)-\left(2x+2\right)\)

\(\Leftrightarrow3x\left(x+1\right)-2x\left(x+1\right)\)

\(\Leftrightarrow\left(x+1\right)\left(3x-2x\right)\)

\(\)

a) x³-10x²+21x
= x³-7x²-3x²+21x
= x²(x-7)-3x(x-7)
= (x²-3x)(x-7)
b) 3x³-7x²-20x
= x(3x²-7x-20)
= x(3x²+5x-12x-20)
= x[x(3x+5)-4(3x+5)]
= x(x-4)(3x+5)

a: Ta có: \(-3x^4+20x^3-35x^2-10x+48\)

\(=-\left(3x^4-20x^3+35x^2+10x-48\right)\)

\(=-\left(3x^4-9x^3-11x^3+33x^2+2x^2-6x+16x-48\right)\)

\(=-\left(x-3\right)\left(3x^3-11x^2+2x+16\right)\)

\(=-\left(x-3\right)\left(3x^3-6x^2-5x^2+10x-8x+16\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x^2-5x-8\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x-8\right)\left(x+1\right)\)

b: Ta có: \(-\left(2x^4+7x^3+x^2-7x-3\right)\)

\(=-\left(2x^4-2x^3+9x^3-9x^2+10x^2-10x+3x-3\right)\)

\(=-\left(x-1\right)\left(2x^3+9x^2+10x+3\right)\)

\(=-\left(x-1\right)\left(2x^3+2x^2+7x^2+7x+3x+3\right)\)

\(=-\left(x-1\right)\left(x+1\right)\left(2x^2+7x+3\right)\)

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

a: =(x+6)(x-1)

n: \(=4x^4+36x^2+81-36x^2\)

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

1)  =\(-3x^4+9x^3+11x^3-33x^2-2x^2+6x-16x+48\)

    =\(-3x^3\left(x-3\right)+11x^2\left(x-3\right)-2x\left(x-3\right)-16\left(x-3\right)\)

=  \(\left(x-3\right)\left(-3x^3+11x^2-2x-16\right)\)

= \(\left(x-3\right)\left(-3x^3+6x^2+5x^2-10x+8x-16\right)\)

=\(\left(x-3\right)\left(-3x^2\left(x-2\right)+5x\left(x-2\right)+8\left(x-2\right)\right)\)

=  \(\left(x-3\right)\left(x-2\right)\left(-3x^2+5x+8\right)\)

= \(\left(x-3\right)\left(x-2\right)\left(x-\frac{8}{3}\right)\left(x+1\right)\)

Ý b lm theo ý tưởng tương tự nha bn :D 

1) x² -7x + 10 = x² - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)

2) x² + 3x + 2 = x² + 2x + x  + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)

3) x² - 7x + 12 = x² - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)

4) x² + 7x + 12 = x² + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)

5) 16x - 5x² - 3 = 15x - 5x² + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x) 

6) 6x² + 7x - 3 = 6x² - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)  

7) 3x² - 3x - 6 = 3x² - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)

8) 3x² + 3x - 6 = 3x² - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)

9) 6x² - 13x + 6 = 6x² - 9x -  4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3) 

10) 6x² + 15x  + 6 = 6x² + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)

11) 6x² - 20x + 6 = 6x² - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)

12) 8x² + 5x - 3 = 8x² + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)

1) x²- 3x - 6x +18 

= (x²- 3x )-(6x -18 )

= x(x-3)- 6(x-3)

= (x-6)(x-3)

\(2,x^2-3x-54\)

\(=x^2-9x+6x-54\)

\(=x\left(x-9\right)+6\left(x-9\right)\)

\(=\left(x+6\right)\left(x-9\right)\)

\(3,20x^2+7x-6\)

\(=20x^2-8x+15x-6\)

\(=4x\left(5x-2\right)+3\left(5x-2\right)\)

\(=\left(4x+3\right)\left(5x-2\right)\)

a. 7x⁵ - 14x³y + 21x²y

= 7x²(x³ - 2xy + 3y)

b. 4x² - 20x + 25

= (2x)² - 2x.2.5 + 5²

= (2x - 5)²

a) \(7x^5-14x^3y+21x^2y\)

\(=7x^2\left(x^3-2xy+3y\right)\)

b) \(4x^2-20x+25\)

\(=\left(2x\right)^2-2.2x.5+5^2\)

\(\left(2x-5\right)^2\)