Q&A

How do you solve for a polynomial?

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How do you solve for a polynomial?

Step by Step

  1. If solving an equation, put it in standard form with 0 on one side and simplify. [
  2. Know how many roots to expect. [
  3. If you’re down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula. [
  4. Find one rational factor or root.
  5. Divide by your factor.

How do you solve a polynomial function in standard form?

The steps to writing the polynomials in standard form are:

  1. Write the terms.
  2. Group all the like terms.
  3. Find the exponent.
  4. Write the term with the highest exponent first.
  5. Write the rest of the terms with lower exponents in descending order.
  6. Write the constant term (a number with no variable) in the end.

How do you find the root of a polynomial with x+1?

By multiplying by x + 1 you introduced this root which is not a root of the original polynomial. So there are no real roots for the polynomial, only complex ones. Hence the final solutions are as follows: x = cos(2k + 1)π 7 + isin(2k + 1)π 7, 0 ≤ k ≤ 6 and k ≠ 3

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What is the degree of the polynomial 3XY?

Consequently the degree of the polynomial in x is 3, the degree in y is 4, and its degree is 5, as indicated in the table above. Any collection of factors in a given monomial is called the coefficient of the remaining factors in the monomial. Thus in the monomial 3 xy,3 is the coefficient of xy, while 3 y is the coefficient of x.

What are the final solutions for the polynomial x = cos(2k + 1)?

So there are no real roots for the polynomial, only complex ones. Hence the final solutions are as follows: x = cos(2k + 1)π 7 + isin(2k + 1)π 7, 0 ≤ k ≤ 6 and k ≠ 3 This equation has the same coefficients read backwards.

How do you find where a polynomial crosses the x axis?

We can enter the polynomial into the Function Grapher, and then zoom in to find where it crosses the x-axis. Graphing is a good way to find approximate answers, and we may also get lucky and discover an exact answer. Caution: before you jump in and graph it, you should really know How Polynomials Behave, so you find all the possible answers!

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