Write as a Set of Linear Factors x^4+5x^3-4x^2-8x+6


Step 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 2
Find every combination of . These are the possible roots of the polynomial function.

Step 3
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 .
Multiply by .
Add and .
Raise to the power of .
Multiply by .
Subtract from .
Multiply by .
Subtract from .
Add and .

Step 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 5
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.
++
-+--+
-+
+-
-+
+-
-+
-
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.

Step 6
Write as a set of factors.


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