not sure how to do this problem.
x^3-6x^2+15x-7=(x+a)^3+bx+c <-- need to find what "a","b", and "c" are. Thank you if you can help me out!
x^3-6x^2+15x-7=(x+a)^3+bx+c <-- need to find what "a","b", and "c" are. Thank you if you can help me out!
-
Well, (x + a)^3 = x^3 + 3x²a + 3a²x + a^3. Since you need this part to include both the x^3 and the x² term, you have no choice but to insist that -6x² = 3x²a. This makes a = -2. Absorb the rest into b and c.
x^3 - 6x² + 15x - 7 = (x - 2)^3 + bx + c
x^3 - 6x² + 15x - 7 = x^3 - 6x² + 12x - 8 + bx + c ==>
15x = (12 + b)x ==> b = 3
-7 = - 8 + c ==> c = 1.
So the solution is a = -2, b = 3, c = 1.
x^3 - 6x² + 15x - 7 = (x - 2)^3 + bx + c
x^3 - 6x² + 15x - 7 = x^3 - 6x² + 12x - 8 + bx + c ==>
15x = (12 + b)x ==> b = 3
-7 = - 8 + c ==> c = 1.
So the solution is a = -2, b = 3, c = 1.