Question

how to solve polynomial equation

Answer 1

Answer:

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Step-by-step explanation:

If solving an equation, put it in standard form with 0 on one side and simplify.   [ details ]

Know how many roots to expect.   [ details ]

If you’re down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula.   [ details ]

Then go to step 7.

Find one rational factor or root. This is the hard part, but there are lots of techniques to help you.   [ details ]

If you can find a factor or root, continue with step 5 below; if you can’t, go to step 6.

Divide by your factor. This leaves you with a new reduced polynomial whose degree is 1 less.   [ details ]  

For the rest of the problem, you’ll work with the reduced polynomial and not the original. Continue at step 3.

If you can’t find a factor or root, turn to numerical methods.   [ details ]

Then go to step 7.

If this was an equation to solve, write down the roots. If it was a polynomial to factor, write it in factored form, including any constant factors you took out in step 1.

Answer 2

Answer:

Step-by-step explanation:

1 . Determine whether you have a linear polynomial. A linear polynomial is a polynomial of the first degree.[1] This means that no variable will have an exponent greater than one. Because this is a first-degree polynomial, it will have exactly one real root, or solution.[2]

For example, 5x+2 is a linear polynomial, because the variable }x has no exponent (which is the same as an exponent of 1).

2 . Set the equation to equal zero. This is a necessary step for solving all polynomials.

For example,5x+2=0

3. Isolate the variable term. To do this, add or subtract the constant from both sides of the equation. A constant is a term without a variable.[3]

For example, to isolate the x term in 5x+2=0, you would subtract  2 from both sides of the equation:

5x+2=0

5x+2-2=0-2

5x=-2

4. Solve for the variable. Usually you will need to divide each side of the equation by the coefficient. This will give you the root, or solution, to your polynomial.

For example, to solve for x in 5x=-2, you would divide each side of the equation by 5:

5x=-2

5x/5 = -2/5

x = -2/5

So, the solution to 5x+2 is x=-2/5