Factor X^3-6x^2+12x-8 - Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Factor x^3-6x^2+12x-8 Step 1Factor using the rational roots test.Tap for more steps...Step 1.1If 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 1.2Find every combination of . These are the possible roots of the polynomial function.Step 1.3Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.Tap for more steps...Step 1.3.1Substitute into the polynomial.Step 1.3.2Raise to the power of .Step 1.3.3Raise to the power of .Step 1.3.4Multiply by .Step 1.3.5Subtract from .Step 1.3.6Multiply by .Step 1.3.7Add and .Step 1.3.8Subtract from .Step 1.4Since 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 1.5Divide by .Tap for more steps...Step 1.5.1Set 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 1.5.2Divide the highest order term in the dividend by the highest order term in divisor .

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Step 1.5.3Multiply the new quotient term by the divisor.

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Step 1.5.4The expression needs to be subtracted from the dividend, so change all the signs in

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Step 1.5.5After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

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Step 1.5.6Pull the next terms from the original dividend down into the current dividend.

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Step 1.5.7Divide the highest order term in the dividend by the highest order term in divisor .

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Step 1.5.8Multiply the new quotient term by the divisor.

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Step 1.5.9The expression needs to be subtracted from the dividend, so change all the signs in

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Step 1.5.10After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

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Step 1.5.11Pull the next terms from the original dividend down into the current dividend.

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Step 1.5.12Divide the highest order term in the dividend by the highest order term in divisor .

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Step 1.5.13Multiply the new quotient term by the divisor.

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Step 1.5.14The expression needs to be subtracted from the dividend, so change all the signs in

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Step 1.5.15After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

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Step 1.5.16Since the remander is , the final answer is the quotient.Step 1.6Write as a set of factors.Step 2Factor using the perfect square rule.Tap for more steps...Step 2.1Rewrite as .Step 2.2Check that the middle term is two times the product of the numbers being squared in the first term and third term.Step 2.3Rewrite the polynomial.Step 2.4Factor using the perfect square trinomial rule , where and .Step 3Combine like factors.Tap for more steps...Step 3.1Raise to the power of .Step 3.2Use the power rule to combine exponents.Step 3.3Add and .

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