### Home > PC > Chapter 6 > Lesson 6.2.3 > Problem 6-100

6-100.

We know that * *=

*x*+

*B*for some numbers

*A*and

*B*. Find

*A*and

*B*. Homework Help ✎

Multiply both sides by (*x* − 1).

*x*^{2} − 3*x* + *A* = (*x* + *B*)(*x* − 1)

Multiply out on the right side.

*x*^{2} − 3*x* + *A* = *x*^{2} + *Bx* − *x* − *B*

Subtract *x*^{2} from both sides.

−3*x* + *A* = *Bx* − *x* − *B*

Subtract *x* from both sides of the equation.

−2*x* + *A* = *Bx* − *B*

Set the *x*-terms = to each other.

Set the constant terms = to each other.

∴ − 2 = *B* and *A* = − *B*

∴ *A* = 2

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