Factor x^3+x^2-5x+3


Step 1
Factor using the rational roots test.

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.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.

Substitute into the polynomial.
Raise to the power of .
Raise to the power of .
Add and .
Multiply by .
Subtract from .
Add and .
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.
Divide by .

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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Divide the highest order term in the dividend by the highest order term in divisor .
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Multiply the new quotient term by the divisor.
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The expression needs to be subtracted from the dividend, so change all the signs in
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After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Pull the next terms from the original dividend down into the current dividend.
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Divide the highest order term in the dividend by the highest order term in divisor .
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Multiply the new quotient term by the divisor.
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The expression needs to be subtracted from the dividend, so change all the signs in
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After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Pull the next terms from the original dividend down into the current dividend.
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Divide the highest order term in the dividend by the highest order term in divisor .
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Multiply the new quotient term by the divisor.
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The expression needs to be subtracted from the dividend, so change all the signs in
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After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Since the remander is , the final answer is the quotient.
Write as a set of factors.

Step 2
Factor using the AC method.

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Remove unnecessary parentheses.

Step 3
Combine like factors.

Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .


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