Factor F(x)=x^4+2x^3-7x^2-8x+12 | Mathway

Enter a problem... Precalculus Examples Popular Problems Precalculus Factor f(x)=x^4+2x^3-7x^2-8x+12 Step 1Regroup terms.Step 2Factor out of .Tap for more steps...Step 2.1Factor out of .Step 2.2Factor out of .Step 2.3Factor out of .Step 3Factor by grouping.Tap for more steps...Step 3.1For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .Tap for more steps...Step 3.1.1Factor out of .Step 3.1.2Rewrite as plus Step 3.1.3Apply the distributive property.Step 3.2Factor out the greatest common factor from each group.Tap for more steps...Step 3.2.1Group the first two terms and the last two terms.Step 3.2.2Factor out the greatest common factor (GCF) from each group.Step 3.3Factor the polynomial by factoring out the greatest common factor, .Step 4Factor out of .Tap for more steps...Step 4.1Factor out of .Step 4.2Factor out of .Step 4.3Factor out of .Step 5Factor.Tap for more steps...Step 5.1Rewrite in a factored form.Tap for more steps...Step 5.1.1Factor using the rational roots test.Tap for more steps...Step 5.1.1.1If 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 5.1.1.2Find every combination of . These are the possible roots of the polynomial function.Step 5.1.1.3Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.Tap for more steps...Step 5.1.1.3.1Substitute into the polynomial.Step 5.1.1.3.2Raise to the power of .Step 5.1.1.3.3Multiply by .Step 5.1.1.3.4Subtract from .Step 5.1.1.3.5Add and .Step 5.1.1.4Since 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 5.1.1.5Divide by .Tap for more steps...Step 5.1.1.5.1Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .

-

+

-

+

Step 5.1.1.5.2Divide the highest order term in the dividend by the highest order term in divisor .

-

+

-

+

Step 5.1.1.5.3Multiply the new quotient term by the divisor.

-	+	-	+
+	-

Step 5.1.1.5.4The expression needs to be subtracted from the dividend, so change all the signs in

-	+	-	+
-	+

Step 5.1.1.5.5After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

-	+	-	+
-	+
+

Step 5.1.1.5.6Pull the next terms from the original dividend down into the current dividend.

-	+	-	+
-	+
+	-

Step 5.1.1.5.7Divide the highest order term in the dividend by the highest order term in divisor .

+
-	+	-	+
-	+
+	-

Step 5.1.1.5.8Multiply the new quotient term by the divisor.

+
-	+	-	+
-	+
+	-
+	-

Step 5.1.1.5.9The expression needs to be subtracted from the dividend, so change all the signs in

+
-	+	-	+
-	+
+	-
-	+

Step 5.1.1.5.10After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

+
-	+	-	+
-	+
+	-
-	+
-

Step 5.1.1.5.11Pull the next terms from the original dividend down into the current dividend.

+
-	+	-	+
-	+
+	-
-	+
-	+

Step 5.1.1.5.12Divide the highest order term in the dividend by the highest order term in divisor .

+	-
-	+	-	+
-	+
+	-
-	+
-	+

Step 5.1.1.5.13Multiply the new quotient term by the divisor.

+	-
-	+	-	+
-	+
+	-
-	+
-	+
-	+

Step 5.1.1.5.14The expression needs to be subtracted from the dividend, so change all the signs in

+	-
-	+	-	+
-	+
+	-
-	+
-	+
+	-

Step 5.1.1.5.15After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

+	-
-	+	-	+
-	+
+	-
-	+
-	+
+	-

Step 5.1.1.5.16Since the remander is , the final answer is the quotient.Step 5.1.1.6Write as a set of factors.Step 5.1.2Factor using the AC method.Tap for more steps...Step 5.1.2.1Factor using the AC method.Tap for more steps...Step 5.1.2.1.1Consider 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 5.1.2.1.2Write the factored form using these integers.Step 5.1.2.2Remove unnecessary parentheses.Step 5.2Remove unnecessary parentheses.

Please ensure that your password is at least 8 characters and contains each of the following:

• a number
• a letter
• a special character: @$#!%*?&