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Completely factor 𝑍 cubed plus six 𝑍 squared plus six plus 𝑍.
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In order to factor, we need to put this in descending order, standard form.
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So the highest power, the highest exponent, will go first, then the next highest and the next highest, and so on.
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So 𝑍 cubed is first, then plus six 𝑍 squared plus 𝑍 plus six.
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Now there are four terms here.
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So we can factor by grouping.
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So we will group the first two terms together and the last two terms together.
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And now we will take a greatest common factor out of each set of parentheses.
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Out of 𝑍 cubed and six 𝑍 squared, we can take out a 𝑍 squared.
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And if we would divide each of these terms by 𝑍 squared — essentially take it out — we will be left with 𝑍 plus six.
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Now out of the next set of parentheses, we can only take out a one.
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So if we would divide each term by one, we will be left with 𝑍 plus six.
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So now our GCFs will become one factor, so 𝑍 squared and positive one.
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And then the matching parentheses will be the other factor, which will be 𝑍 plus six.
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Therefore, after completely factoring, we get an answer of 𝑍 squared plus one times 𝑍 plus six.