Finding values a, b for (x^2+a)(2x-b) = 2x^3 - 3x^2 + 4x - 6

[sznaiden]

 

[Steven G]

In your last line--
1) The coefficient of x^3 on each side of the equal sign must be equal.
2) The coefficient of x^2 on each side of the equal sign must be equal.
3) The coefficient of x on each side of the equal sign must be equal.
4) The coefficient of the constant on each side of the equal sign must be equal.

 

[topsquark]

View attachment 34855

You have the system of equations
-b = -3
2a = 4
-ba = -6
What are a and b?

-Dan

 

[Steven G]

You have the system of equations
-b = -3
2a = 4
-ba = -6
What are a and b?

-Dan

For OP:
When you are comparing the coefficient of like terms you can just equate what comes after the subtraction sign, just like you do after the addition sign.

In this case, we immediately get b=3