a: \(P=x^2-5x+6\)

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

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

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

b: \(P=3x^2+14x-5\)

\(=3x^2+15x-x-5\)

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

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

c: \(P=-2x^2-7x-5\)

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

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

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

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

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

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. 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: \(-6x^2+7x-2\)

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

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

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

b: \(2x^2-5x+2\)

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

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

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

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

a: \(=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)

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

\(=\left(x^2y^2-9\right)\left(x^2y^2-7\right)\)

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

c: \(=x^2-8x+x-8\)

\(=x\left(x-8\right)+\left(x-8\right)\)

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

\(a,xy+y^2-x-y\)

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

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

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

\(---\)

\(b,\left(x^2y^2-8\right)^2-1\)

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

\(=\left[\left(xy\right)^2-9\right]\left(x^2y^2-7\right)\)

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

\(---\)

\(c,x^2-7x-8\)

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

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

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

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

\(Toru\)

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

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

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

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