Questions: Factor the polynomial. bc-a-ba+c bc-a-ba+c=

Solution Steps

To factor the given polynomial \( bc - a - ba + c \), we can look for common factors in pairs of terms and then apply the distributive property. First, group the terms as \((bc - ba) + (c - a)\). Then, factor out the common factors from each group.

We start with the polynomial given in the problem: \[ bc - a - ba + c \] This can be rearranged as: \[ -ba + bc - a + c \]

Next, we group the terms to facilitate factoring: \[ (bc - ba) + (c - a) \]

Now, we factor out the common factors from each group:

1. From the first group \(bc - ba\), we can factor out \(b\): \[ b(c - a) \]
2. From the second group \(c - a\), we can factor out \(-1\): \[ -(a - c) \]

Combining the factored groups, we have: \[ b(c - a) - (a - c) \] This can be rewritten as: \[ -(a - c)(b + 1) \]

Final Answer