Factor two x to the power of four minus x to the power of three minus fifty-one x to the power of two plus twenty-five x plus twenty-five

Factor 2x^4-x^3-51x^2+25x+25
Regroup terms.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Rewrite as .
Let . Substitute for all occurrences of .
Factor by grouping.
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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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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Rewrite as .
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Let . Substitute for all occurrences of .
Factor by grouping.
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Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Factor out of .
Rewrite as plus
Apply the distributive property.
Multiply by .
Factor out the greatest common factor from each group.
Tap for more steps...
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Factor.
Tap for more steps...
Replace all occurrences of with .
Remove unnecessary parentheses.
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