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Note: Make sure to fully factor each of the below. Remember that, factor by
grouping is just one step in the factoring process, you should check any resulting
factors you get after factor by grouping (or any other factoring method) to see if they
are still factorable.
1 : Factor the following polynomial:
You want to factor by grouping, so you
want to group up terms into pairs and then factor out any common terms from each
pair. For example, if you had then you could group it as , then factor out
any common factors in each group; , then pull out the common term in the
parentheses (only works if they are the same!) to get . This isn’t the end though;
you need to fully factor, so you need to check both terms to see if either is
factorable, in this case is factorable to which gets you as your final factoring.
2 : Factor the following polynomial:
You want to factor by grouping, so you
want to group up terms into pairs and then factor out any common terms from each
pair. For example, if you had then you could group it as , then factor out
any common factors in each group; , then pull out the common term in the
parentheses (only works if they are the same!) to get . This isn’t the end though;
you need to fully factor, so you need to check both terms to see if either is
factorable, in this case is factorable to which gets you as your final factoring.
3 : Factor the following polynomial:
You want to factor by grouping, so you
want to group up terms into pairs and then factor out any common terms from each
pair. For example, if you had then you could group it as , then factor out
any common factors in each group; , then pull out the common term in the
parentheses (only works if they are the same!) to get . This isn’t the end though;
you need to fully factor, so you need to check both terms to see if either is
factorable, in this case is factorable to which gets you as your final factoring.
4 : Factor the following polynomial:
You want to factor by grouping, so you
want to group up terms into pairs and then factor out any common terms from each
pair. For example, if you had then you could group it as , then factor out
any common factors in each group; , then pull out the common term in the
parentheses (only works if they are the same!) to get . This isn’t the end though;
you need to fully factor, so you need to check both terms to see if either is
factorable, in this case is factorable to which gets you as your final factoring.
5 : Factor the following polynomial:
You want to factor by grouping, so you
want to group up terms into pairs and then factor out any common terms from each
pair. For example, if you had then you could group it as , then factor out
any common factors in each group; , then pull out the common term in the
parentheses (only works if they are the same!) to get . This isn’t the end though;
you need to fully factor, so you need to check both terms to see if either is
factorable, in this case is factorable to which gets you as your final factoring.