Precalculus Examples

Factor 2x^4-x^3-19x^2+9x+9
Step 1
Regroup terms.
Step 2
Factor out of .
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
Step 3
Rewrite as .
Step 4
Factor.
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Step 4.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4.2
Remove unnecessary parentheses.
Step 5
Rewrite as .
Step 6
Let . Substitute for all occurrences of .
Step 7
Factor by grouping.
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Step 7.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 7.1.1
Factor out of .
Step 7.1.2
Rewrite as plus
Step 7.1.3
Apply the distributive property.
Step 7.2
Factor out the greatest common factor from each group.
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Step 7.2.1
Group the first two terms and the last two terms.
Step 7.2.2
Factor out the greatest common factor (GCF) from each group.
Step 7.3
Factor the polynomial by factoring out the greatest common factor, .
Step 8
Replace all occurrences of with .
Step 9
Rewrite as .
Step 10
Factor.
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Step 10.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 10.2
Remove unnecessary parentheses.
Step 11
Factor out of .
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Step 11.1
Factor out of .
Step 11.2
Factor out of .
Step 11.3
Factor out of .
Step 12
Let . Substitute for all occurrences of .
Step 13
Factor by grouping.
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Step 13.1
Reorder terms.
Step 13.2
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 13.2.1
Factor out of .
Step 13.2.2
Rewrite as plus
Step 13.2.3
Apply the distributive property.
Step 13.2.4
Multiply by .
Step 13.3
Factor out the greatest common factor from each group.
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Step 13.3.1
Group the first two terms and the last two terms.
Step 13.3.2
Factor out the greatest common factor (GCF) from each group.
Step 13.4
Factor the polynomial by factoring out the greatest common factor, .
Step 14
Factor.
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Step 14.1
Replace all occurrences of with .
Step 14.2
Remove unnecessary parentheses.