Factor P(x)=x^3-7x+6


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 .
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 .
-+-+
Divide the highest order term in the dividend by the highest order term in divisor .
-+-+
Multiply the new quotient term by the divisor.
-+-+
+-
The expression needs to be subtracted from the dividend, so change all the signs in
-+-+
-+
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-+-+
-+
+
Pull the next terms from the original dividend down into the current dividend.
-+-+
-+
+-
Divide the highest order term in the dividend by the highest order term in divisor .
+
-+-+
-+
+-
Multiply the new quotient term by the divisor.
+
-+-+
-+
+-
+-
The expression needs to be subtracted from the dividend, so change all the signs in
+
-+-+
-+
+-
-+
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+
-+-+
-+
+-
-+
-
Pull the next terms from the original dividend down into the current dividend.
+
-+-+
-+
+-
-+
-+
Divide the highest order term in the dividend by the highest order term in divisor .
+-
-+-+
-+
+-
-+
-+
Multiply the new quotient term by the divisor.
+-
-+-+
-+
+-
-+
-+
-+
The expression needs to be subtracted from the dividend, so change all the signs in
+-
-+-+
-+
+-
-+
-+
+-
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+-
-+-+
-+
+-
-+
-+
+-
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.


Related Questions