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Completely factor 𝑧𝑏 − 𝑧𝑥 + 𝑏 − 𝑥.
Completely factor 𝑧𝑏 minus 𝑧𝑥 plus 𝑏 minus 𝑥.
Since there are four terms, we can factor by grouping. So we begin by grouping the first two terms together and the last two terms together. And now, we take out our greatest common factor from each set of parentheses.
From the first parentheses, we can take out a 𝑧. And after we do, we are left with 𝑏 minus 𝑥. Out of the second parentheses, we can take out a one. And after doing so, we’re left with 𝑏 minus 𝑥.
So the greatest common factors come together to be one factor. So we’ve 𝑧 plus one and the matching parentheses come together to be a factor — so 𝑏 minus 𝑥.
So after completely factoring, we will get 𝑧 plus one times 𝑏 minus 𝑥.