Algebra Examples

Factor x^3-2x^2-5x+6
Step 1
Factor using the rational roots test.
Tap for more steps...
Step 1.1
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 1.2
Find every combination of . These are the possible roots of the polynomial function.
Step 1.3
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Tap for more steps...
Step 1.3.1
Substitute into the polynomial.
Step 1.3.2
Raise to the power of .
Step 1.3.3
Raise to the power of .
Step 1.3.4
Multiply by .
Step 1.3.5
Subtract from .
Step 1.3.6
Multiply by .
Step 1.3.7
Subtract from .
Step 1.3.8
Add and .
Step 1.4
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 1.5
Divide by .
Tap for more steps...
Step 1.5.1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
---+
Step 1.5.2
Divide the highest order term in the dividend by the highest order term in divisor .
---+
Step 1.5.3
Multiply the new quotient term by the divisor.
---+
+-
Step 1.5.4
The expression needs to be subtracted from the dividend, so change all the signs in
---+
-+
Step 1.5.5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
---+
-+
-
Step 1.5.6
Pull the next terms from the original dividend down into the current dividend.
---+
-+
--
Step 1.5.7
Divide the highest order term in the dividend by the highest order term in divisor .
-
---+
-+
--
Step 1.5.8
Multiply the new quotient term by the divisor.
-
---+
-+
--
-+
Step 1.5.9
The expression needs to be subtracted from the dividend, so change all the signs in
-
---+
-+
--
+-
Step 1.5.10
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-
---+
-+
--
+-
-
Step 1.5.11
Pull the next terms from the original dividend down into the current dividend.
-
---+
-+
--
+-
-+
Step 1.5.12
Divide the highest order term in the dividend by the highest order term in divisor .
--
---+
-+
--
+-
-+
Step 1.5.13
Multiply the new quotient term by the divisor.
--
---+
-+
--
+-
-+
-+
Step 1.5.14
The expression needs to be subtracted from the dividend, so change all the signs in
--
---+
-+
--
+-
-+
+-
Step 1.5.15
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
--
---+
-+
--
+-
-+
+-
Step 1.5.16
Since the remander is , the final answer is the quotient.
Step 1.6
Write as a set of factors.
Step 2
Factor using the AC method.
Tap for more steps...
Step 2.1
Factor using the AC method.
Tap for more steps...
Step 2.1.1
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 .
Step 2.1.2
Write the factored form using these integers.
Step 2.2
Remove unnecessary parentheses.