(x+5)(x+2)(x+a) = x^3 + bx^2 + cx - 30



First you expand the triple brackets to get;

x^3 + 5x^2 + 2x^2 + 10x + ax^2 + 5ax + 2ax + 10a = x^3 + bx^2 + cx - 30



You can now cancel down the equation to get;

7x^2 + 10x + ax^2 + 7ax + 10a = bx^2 + cx - 30



Next you find 10a.

So 10a = -30 so a = -3 because 10 x -3 = -30



Then, you split the equations;

7x^2 + ax^2 = bx^2 & 10x + 7ax = cx



Now, you can factor in -3 to the equations containing 'a' to get;

7x^2 - 3x^2 = bx^2 so b = 4 because 7 - 3 = 4



and you also get;

10x + 7ax = cx so c = -11 because 7 x -3 = -21. Then you do 10 + -21 to get -11.



So the answers to (x+5)(x+2)(x+a) = x^3 + bx^2 + cx - 30 are;

a = -3

b = 4

c = -11



Hope this helps :)