# Find the Roots (Zeros) x^3-7x+6=0

Factor the left side of the equation.

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Factor using the rational roots test.

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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.

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Substitute into the polynomial.

Raise to the power of .

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 .

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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.

Factor using the AC method.

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Factor using the AC method.

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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.

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set equal to and solve for .

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Set equal to .

Add to both sides of the equation.

Set equal to and solve for .

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Set equal to .

Add to both sides of the equation.

Set equal to and solve for .

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Set equal to .

Subtract from both sides of the equation.

The final solution is all the values that make true.

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