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) \(3x^2-7x+2=3x^2-6x-x+2=3x\left(x-2\right)-\left(x-2\right)=\left(x-2\right)\left(3x-1\right)=\left(x-2\right)\left(x-\dfrac{1}{3}\right)\)

`-x^2 +7x-6`

`=-x^2 +6x+x-6`

`=x(6-x)-(6-x)`

`=(x-1)(6-x)`

=-(x^2-7x+6)

=-(x-1)(x-6)

\(2x^2-7x+5=\left(2x^2-2x\right)-\left(5x-5\right)=2x\left(x-1\right)-5\left(x-1\right)=\left(2x-5\right)\left(x-1\right)\)

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

a: \(2x^2-7x+5=\left(x-1\right)\left(2x-5\right)\)

b: \(3x^2+5x+2=\left(x+1\right)\left(3x+2\right)\)

a: \(-6x^2+7x-2\)

\(=-6x^2+3x+4x-2\)

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

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

b: \(2x^2-5x+2\)

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

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

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

a: \(P=2x^2-7x+6\)

\(=2x^2-4x-3x+6\)

\(=2x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\left(2x-3\right)\)

b: \(P=2x^2-7x+3\)

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

\(=2x\left(x-3\right)-\left(x-3\right)\)

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

c: \(P=2x^2+9x-5\)

\(=2x^2+10x-x-5\)

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

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

a) 7x – 14 = 7(x - 2)

b) 5x3 - 10x2y +5xy2 = 5x(x² - 2xy - y²) = 5x(x - y)²

c) 25 – x2= (x - 5)(x + 5)

a, \(7\left(x-2\right)\)

c, \(\left(5-x\right)\left(5+x\right)\)

 \(a,7x-14=7\left(x-2\right)\\ b.5x^3-10x^2y+5xy^2=5x\left(x^2-2xy+y^2\right)=5x\left(x-y\right)^2\\ c,25-x^2=\left(5-x\right)\left(5+x\right)\)

a, 7x - 14 = 7 ( x - 2 )

b, 5x³ - 10x²y + 5xy² 

= 5x ( x² - 2xy + y² ) 

= 5x ( x - y )²

c, 25 - x² = 5² - x² = ( 5 - x ) ( 5 + x )

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) \(4x^2-20x+25\)

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

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

\(a,=7xy\left(x^2-2xy+y^2\right)=7xy\left(x-y\right)^2\\ b,=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\\ c,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\)