Anonymous

x^3-6x^2+9x+8=x(x+a)^2+b identically => LHS=x^3+2ax^2+(a^2)x+b => 2a=-6 b=8 (by comparing the coefficients) => a=-3 b=8

Anonymous

x^3-6x^2+9x+8 = x(x^2+2ax+a^2) + b x^3-6x^2+9x+8 = x^3+2ax^2+a^2 x + b Equate the coefficients of x^2 from both sides -6 = 2a a= -3 Equate the constant terms 8 = b

Anonymous

x³ - 6x² + 9x + 8 = x.(x + a)² + b → you expand the right side x³ - 6x² + 9x + 8 = x.(x² + 2ax + a²) + b x³ - 6x² + 9x + 8 = x³ + 2ax² + a²x + b → you compare both sides 8 = b 9 = a² → a = ± 3 - 6 = 2a → a = - 3 Resume: a = - 3 b = 8

Anonymous

x^3 - 6x^2 + 9x + 8 = x(x + a)^2 + b x(x^2 - 6x + 9) + 8 = x(x + a)^2 + b x (x - 3)^2 + 8 = x(x + a)^2 + b a = -3, b = 8

Anonymous

x^3-6x^2+9x+8 = x(x-3)^2+8

Anonymous

(x + a)^2 = (x + a)(x + a) = x^2 + 2ax + a^2 x(x^2 + 2ax + a^2) + b = x^3 + 2ax^2 + xa^2 + b So, 2a = -6 makes a = -3 and 8 = b

Anonymous

x³-6x²+9x+8 = x(x+a)²+b x³-6x²+9x+8 = x(x²+a²+2ax)+b x³-6x²+9x+8 = x³+xa²+2ax²+b x³-6x²+9x+8 = x³+2ax²+a²x+b coefficients must match –6 = 2a 9 = a² 8 = b a = –3 b = 8