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Basic Math Examples
Step 1
Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out of .
Step 1.4
Factor out of .
Step 1.5
Factor out of .
Step 1.6
Factor out of .
Step 1.7
Factor out of .
Step 2
Regroup terms.
Step 3
Reorder terms.
Step 4
Step 4.1
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Step 4.2
Find every combination of . These are the possible roots of the polynomial function.
Step 4.3
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Step 4.3.1
Substitute into the polynomial.
Step 4.3.2
Raise to the power of .
Step 4.3.3
Multiply by .
Step 4.3.4
Raise to the power of .
Step 4.3.5
Multiply by .
Step 4.3.6
Add and .
Step 4.3.7
Subtract from .
Step 4.4
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Step 4.5
Divide by .
Step 4.5.1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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Step 4.5.2
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 4.5.3
Multiply the new quotient term by the divisor.
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Step 4.5.4
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 4.5.5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 4.5.6
Pull the next terms from the original dividend down into the current dividend.
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Step 4.5.7
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 4.5.8
Multiply the new quotient term by the divisor.
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Step 4.5.9
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 4.5.10
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 4.5.11
Pull the next terms from the original dividend down into the current dividend.
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Step 4.5.12
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 4.5.13
Multiply the new quotient term by the divisor.
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Step 4.5.14
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 4.5.15
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 4.5.16
Pull the next terms from the original dividend down into the current dividend.
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Step 4.5.17
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 4.5.18
Multiply the new quotient term by the divisor.
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Step 4.5.19
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 4.5.20
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 4.5.21
Pull the next terms from the original dividend down into the current dividend.
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Step 4.5.22
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 4.5.23
Multiply the new quotient term by the divisor.
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Step 4.5.24
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 4.5.25
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 4.5.26
Since the remander is , the final answer is the quotient.
Step 4.6
Write as a set of factors.
Step 5
Step 5.1
Reorder and .
Step 5.2
Factor out of .
Step 5.3
Factor out of .
Step 5.4
Factor out of .
Step 6
Expand by multiplying each term in the first expression by each term in the second expression.
Step 7
Step 7.1
Reorder the factors in the terms and .
Step 7.2
Add and .
Step 7.3
Add and .
Step 8
Step 8.1
Rewrite using the commutative property of multiplication.
Step 8.2
Multiply by by adding the exponents.
Step 8.2.1
Move .
Step 8.2.2
Multiply by .
Step 8.2.2.1
Raise to the power of .
Step 8.2.2.2
Use the power rule to combine exponents.
Step 8.2.3
Add and .
Step 8.3
Multiply by .
Step 8.4
Rewrite using the commutative property of multiplication.
Step 8.5
Multiply by by adding the exponents.
Step 8.5.1
Move .
Step 8.5.2
Multiply by .
Step 8.5.2.1
Raise to the power of .
Step 8.5.2.2
Use the power rule to combine exponents.
Step 8.5.3
Add and .
Step 8.6
Multiply by .
Step 8.7
Rewrite using the commutative property of multiplication.
Step 8.8
Multiply by by adding the exponents.
Step 8.8.1
Move .
Step 8.8.2
Multiply by .
Step 8.8.2.1
Raise to the power of .
Step 8.8.2.2
Use the power rule to combine exponents.
Step 8.8.3
Add and .
Step 8.9
Multiply by .
Step 8.10
Rewrite using the commutative property of multiplication.
Step 8.11
Multiply by by adding the exponents.
Step 8.11.1
Move .
Step 8.11.2
Multiply by .
Step 8.12
Multiply by .
Step 8.13
Multiply by .
Step 8.14
Multiply by .
Step 8.15
Multiply by .
Step 8.16
Multiply by .
Step 9
Step 9.1
Add and .
Step 9.2
Add and .
Step 9.3
Add and .
Step 9.4
Add and .
Step 10
Add and .
Step 11
Step 11.1
Reorder terms.
Step 11.2
Remove unnecessary parentheses.
Step 12
Factor out negative.
Step 13
Remove unnecessary parentheses.