Precalculus Examples

Find the Degree f(x)=2x^2(x-1)(x+2)^3(x^2+1)^2
Step 1
Simplify and reorder the polynomial.
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Step 1.1
Apply the distributive property.
Step 1.2
Multiply by by adding the exponents.
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Step 1.2.1
Move .
Step 1.2.2
Multiply by .
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Step 1.2.2.1
Raise to the power of .
Step 1.2.2.2
Use the power rule to combine exponents.
Step 1.2.3
Add and .
Step 1.3
Multiply by .
Step 1.4
Use the Binomial Theorem.
Step 1.5
Simplify each term.
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Step 1.5.1
Multiply by .
Step 1.5.2
Raise to the power of .
Step 1.5.3
Multiply by .
Step 1.5.4
Raise to the power of .
Step 1.6
Expand by multiplying each term in the first expression by each term in the second expression.
Step 1.7
Simplify terms.
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Step 1.7.1
Simplify each term.
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Step 1.7.1.1
Multiply by by adding the exponents.
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Step 1.7.1.1.1
Move .
Step 1.7.1.1.2
Use the power rule to combine exponents.
Step 1.7.1.1.3
Add and .
Step 1.7.1.2
Rewrite using the commutative property of multiplication.
Step 1.7.1.3
Multiply by by adding the exponents.
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Step 1.7.1.3.1
Move .
Step 1.7.1.3.2
Use the power rule to combine exponents.
Step 1.7.1.3.3
Add and .
Step 1.7.1.4
Multiply by .
Step 1.7.1.5
Rewrite using the commutative property of multiplication.
Step 1.7.1.6
Multiply by by adding the exponents.
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Step 1.7.1.6.1
Move .
Step 1.7.1.6.2
Multiply by .
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Step 1.7.1.6.2.1
Raise to the power of .
Step 1.7.1.6.2.2
Use the power rule to combine exponents.
Step 1.7.1.6.3
Add and .
Step 1.7.1.7
Multiply by .
Step 1.7.1.8
Multiply by .
Step 1.7.1.9
Multiply by by adding the exponents.
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Step 1.7.1.9.1
Move .
Step 1.7.1.9.2
Use the power rule to combine exponents.
Step 1.7.1.9.3
Add and .
Step 1.7.1.10
Rewrite using the commutative property of multiplication.
Step 1.7.1.11
Multiply by by adding the exponents.
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Step 1.7.1.11.1
Move .
Step 1.7.1.11.2
Use the power rule to combine exponents.
Step 1.7.1.11.3
Add and .
Step 1.7.1.12
Multiply by .
Step 1.7.1.13
Rewrite using the commutative property of multiplication.
Step 1.7.1.14
Multiply by by adding the exponents.
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Step 1.7.1.14.1
Move .
Step 1.7.1.14.2
Multiply by .
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Step 1.7.1.14.2.1
Raise to the power of .
Step 1.7.1.14.2.2
Use the power rule to combine exponents.
Step 1.7.1.14.3
Add and .
Step 1.7.1.15
Multiply by .
Step 1.7.1.16
Multiply by .
Step 1.7.2
Simplify by adding terms.
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Step 1.7.2.1
Subtract from .
Step 1.7.2.2
Subtract from .
Step 1.7.2.3
Subtract from .
Step 1.7.2.4
Rewrite as .
Step 1.8
Expand using the FOIL Method.
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Step 1.8.1
Apply the distributive property.
Step 1.8.2
Apply the distributive property.
Step 1.8.3
Apply the distributive property.
Step 1.9
Simplify and combine like terms.
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Step 1.9.1
Simplify each term.
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Step 1.9.1.1
Multiply by by adding the exponents.
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Step 1.9.1.1.1
Use the power rule to combine exponents.
Step 1.9.1.1.2
Add and .
Step 1.9.1.2
Multiply by .
Step 1.9.1.3
Multiply by .
Step 1.9.1.4
Multiply by .
Step 1.9.2
Add and .
Step 1.10
Expand by multiplying each term in the first expression by each term in the second expression.
Step 1.11
Simplify terms.
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Step 1.11.1
Simplify each term.
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Step 1.11.1.1
Multiply by by adding the exponents.
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Step 1.11.1.1.1
Move .
Step 1.11.1.1.2
Use the power rule to combine exponents.
Step 1.11.1.1.3
Add and .
Step 1.11.1.2
Rewrite using the commutative property of multiplication.
Step 1.11.1.3
Multiply by by adding the exponents.
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Step 1.11.1.3.1
Move .
Step 1.11.1.3.2
Use the power rule to combine exponents.
Step 1.11.1.3.3
Add and .
Step 1.11.1.4
Multiply by .
Step 1.11.1.5
Multiply by .
Step 1.11.1.6
Multiply by by adding the exponents.
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Step 1.11.1.6.1
Move .
Step 1.11.1.6.2
Use the power rule to combine exponents.
Step 1.11.1.6.3
Add and .
Step 1.11.1.7
Rewrite using the commutative property of multiplication.
Step 1.11.1.8
Multiply by by adding the exponents.
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Step 1.11.1.8.1
Move .
Step 1.11.1.8.2
Use the power rule to combine exponents.
Step 1.11.1.8.3
Add and .
Step 1.11.1.9
Multiply by .
Step 1.11.1.10
Multiply by .
Step 1.11.1.11
Multiply by by adding the exponents.
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Step 1.11.1.11.1
Move .
Step 1.11.1.11.2
Use the power rule to combine exponents.
Step 1.11.1.11.3
Add and .
Step 1.11.1.12
Rewrite using the commutative property of multiplication.
Step 1.11.1.13
Multiply by by adding the exponents.
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Step 1.11.1.13.1
Move .
Step 1.11.1.13.2
Use the power rule to combine exponents.
Step 1.11.1.13.3
Add and .
Step 1.11.1.14
Multiply by .
Step 1.11.1.15
Multiply by .
Step 1.11.1.16
Multiply by by adding the exponents.
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Step 1.11.1.16.1
Move .
Step 1.11.1.16.2
Use the power rule to combine exponents.
Step 1.11.1.16.3
Add and .
Step 1.11.1.17
Rewrite using the commutative property of multiplication.
Step 1.11.1.18
Multiply by by adding the exponents.
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Step 1.11.1.18.1
Move .
Step 1.11.1.18.2
Use the power rule to combine exponents.
Step 1.11.1.18.3
Add and .
Step 1.11.1.19
Multiply by .
Step 1.11.1.20
Multiply by .
Step 1.11.1.21
Multiply by by adding the exponents.
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Step 1.11.1.21.1
Move .
Step 1.11.1.21.2
Use the power rule to combine exponents.
Step 1.11.1.21.3
Add and .
Step 1.11.1.22
Rewrite using the commutative property of multiplication.
Step 1.11.1.23
Multiply by by adding the exponents.
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Step 1.11.1.23.1
Move .
Step 1.11.1.23.2
Use the power rule to combine exponents.
Step 1.11.1.23.3
Add and .
Step 1.11.1.24
Multiply by .
Step 1.11.1.25
Multiply by .
Step 1.11.2
Simplify by adding terms.
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Step 1.11.2.1
Add and .
Step 1.11.2.2
Add and .
Step 1.11.2.3
Subtract from .
Step 1.11.2.4
Subtract from .
Step 1.11.2.5
Subtract from .
Step 1.11.2.6
Subtract from .
Step 2
The largest exponent is the degree of the polynomial.