(1) x3+6x2+9x=x(x2+6x+9)=x(x+3)2x^3 + 6x^2 + 9x = x(x^2 + 6x + 9) = x(x + 3)^2x3+6x2+9x=x(x2+6x+9)=x(x+3)2 (2) a2+b2−c2−2ab=(a−b)2−c2=(a−b−c)(a−b+c)a^2 + b^2 - c^2 - 2ab = (a - b)^2 - c^2 = (a - b - c)(a - b + c)a2+b2−c2−2ab=(a−b)2−c2=(a−b−c)(a−b+c) (3) x3+x2−x−1=(x−1)(x2+2x+1)=(x−1)(x+1)2x^3 + x^2 - x - 1 = (x - 1)(x^2 + 2x + 1) = (x - 1)(x + 1)^2x3+x2−x−1=(x−1)(x2+2x+1)=(x−1)(x+1)2 (4) a2−11ab+24b2=(a−8b)(a−3b)a^2 - 11ab + 24b^2 = (a - 8b)(a - 3b)a2−11ab+24b2=(a−8b)(a−3b) (5) 13x2+73x+4=13(x2+7x+12)=13(x+3)(x+4)\frac{1}{3}x^2 + \frac{7}{3}x + 4 = \frac{1}{3}(x^2 + 7x + 12) = \frac{1}{3}(x + 3)(x + 4)31x2+37x+4=31(x2+7x+12)=31(x+3)(x+4) (6) 6a2−19ab+10b2=(3a−2b)(2a−5b)6a^2 - 19ab + 10b^2 = (3a - 2b)(2a - 5b)6a2−19ab+10b2=(3a−2b)(2a−5b)