I Googled A 2 F, as on that boat, Astrid. And I got this: -
A1) Showing that (x+2) is a factor of f(x). General Method: If A is a number, then (x- A) is a factor of f(x) if when x=A, f(x=A)=0 A = -2 f(x=A = -2) = (-2)^3 - 19(-2) - 30 = -8 + 38 - 30 = 38 - 38 =0. A2) To factorise completely: We know that f(x) = (x+2) x (some other function) The largest term in f(x) = x^3, so f(x) = (x+2)(ax^2 + bx + c) = x^3 - 19x - 30 Multiplying out & comparing terms: ax^3 + bx^2 +cx + 2ax^2 +2bx + 2c = ax^3+x^2(b+2a) + x(c+2b) + 2c = x^3 - 19x - 30 a=1 , b+2a= b+2=0 => b = -2 , c+2b = c + 2(-2) = c - 4 = -19 => c= -15 Therefore: f(x) = (x+2)(x^2 - 2x - 15) We can factorise further (x^2 - 2x - 15) = (x+d)(x+e) comparing terms in a similar way as before leads to final factorisation of f(x) = (x+2)(x-5)(x+3)
Obvious isn't it..
Picturit: You might be right, Chris. With the emphasis on 'might'....the calculation is correct though and when you have some wool it ends up as a sweater.....
Thank you, Chris
Astrid.
Bein an unincorporated city sounds serious., they need to get that sorted out. I know a bloke who lives South of the border down USA way, who likes to sort things out.