Find The Roots (Zeros) F(x)=x^3+4x^2+x-6 | Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Find the Roots (Zeros) f(x)=x^3+4x^2+x-6 Step 1Set equal to .Step 2Solve for .Tap for more steps...Step 2.1Factor the left side of the equation.Tap for more steps...Step 2.1.1Factor using the rational roots test.Tap for more steps...Step 2.1.1.1If 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 2.1.1.2Find every combination of . These are the possible roots of the polynomial function.Step 2.1.1.3Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.Tap for more steps...Step 2.1.1.3.1Substitute into the polynomial.Step 2.1.1.3.2Raise to the power of .Step 2.1.1.3.3Raise to the power of .Step 2.1.1.3.4Multiply by .Step 2.1.1.3.5Add and .Step 2.1.1.3.6Add and .Step 2.1.1.3.7Subtract from .Step 2.1.1.4Since 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 2.1.1.5Divide by .Tap for more steps...Step 2.1.1.5.1Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .

-

+

+

-

Step 2.1.1.5.2Divide the highest order term in the dividend by the highest order term in divisor .

-

+

+

-

Step 2.1.1.5.3Multiply the new quotient term by the divisor.

-	+	+	-
+	-

Step 2.1.1.5.4The expression needs to be subtracted from the dividend, so change all the signs in

-	+	+	-
-	+

Step 2.1.1.5.5After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

-	+	+	-
-	+
+

Step 2.1.1.5.6Pull the next terms from the original dividend down into the current dividend.

-	+	+	-
-	+
+	+

Step 2.1.1.5.7Divide the highest order term in the dividend by the highest order term in divisor .

+
-	+	+	-
-	+
+	+

Step 2.1.1.5.8Multiply the new quotient term by the divisor.

+
-	+	+	-
-	+
+	+
+	-

Step 2.1.1.5.9The expression needs to be subtracted from the dividend, so change all the signs in

+
-	+	+	-
-	+
+	+
-	+

Step 2.1.1.5.10After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

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

Step 2.1.1.5.11Pull the next terms from the original dividend down into the current dividend.

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

Step 2.1.1.5.12Divide the highest order term in the dividend by the highest order term in divisor .

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

Step 2.1.1.5.13Multiply the new quotient term by the divisor.

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

Step 2.1.1.5.14The expression needs to be subtracted from the dividend, so change all the signs in

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

Step 2.1.1.5.15After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

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

Step 2.1.1.5.16Since the remander is , the final answer is the quotient.Step 2.1.1.6Write as a set of factors.Step 2.1.2Factor using the AC method.Tap for more steps...Step 2.1.2.1Factor using the AC method.Tap for more steps...Step 2.1.2.1.1Consider 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 2.1.2.1.2Write the factored form using these integers.Step 2.1.2.2Remove unnecessary parentheses.Step 2.2If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .Step 2.3Set equal to and solve for .Tap for more steps...Step 2.3.1Set equal to .Step 2.3.2Add to both sides of the equation.Step 2.4Set equal to and solve for .Tap for more steps...Step 2.4.1Set equal to .Step 2.4.2Subtract from both sides of the equation.Step 2.5Set equal to and solve for .Tap for more steps...Step 2.5.1Set equal to .Step 2.5.2Subtract from both sides of the equation.Step 2.6The final solution is all the values that make true.Step 3

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

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