How do you solve for x in a 3rd degree polynomial?

Starts here8:22How to Solve a 3rd Degree Polynomial Equation in 5 StepsYouTubeStart of suggested clipEnd of suggested clip59 second suggested clipThis is fairly simple equation to solve we can just subtract 3 from both sides of the equation. AndMoreThis is fairly simple equation to solve we can just subtract 3 from both sides of the equation. And then divide. By to get x equals negative three halves. This is one of the solutions to the equation.

How do you factor a 3rd degree polynomial?

For sums, (x³ + y³) = (x + y) (x² – xy + y²). For differences, (x³ – y³) = (x – y) (x² + xy + y²). For example, let G(x) = 8x³ – 125. Then factoring this third degree polynomial relies on a difference of cubes as follows: (2x – 5) (4x² + 10x + 25), where 2x is the cube-root of 8x³ and 5 is the cube-root of 125.

What is an example of a 3rd degree polynomial?

Answer: The third-degree polynomial is a polynomial in which the degree of the highest term is 3. Explanation: Example: 5×3 + 2×2+ 3x + 7 is a cubic polynomial or Third Degree Polynomial since the highest degree of the expression is 3 or the power of the leading term is 3.

How do you find the third degree of an equation?

A cubic equation is an algebraic equation of third-degree. The general form of a cubic function is: f (x) = ax3 + bx2 + cx1 + d. And the cubic equation has the form of ax3 + bx2 + cx + d = 0, where a, b and c are the coefficients and d is the constant.

Can a third degree polynomial have 2 x intercepts?

The graph of a third degree polynomial f(x) has exactly two x-intercepts. The x-intercepts are -3 and 2. Use this information to come up with an equation for the polynomial function f(x). Use a graph to justify your answer.

How do you find the zeros of a third degree polynomial?

How To: Given a factor and a third-degree polynomial, use the Factor Theorem to factor the polynomial

1. Use synthetic division to divide the polynomial by (x−k) .
2. Confirm that the remainder is 0.
3. Write the polynomial as the product of (x−k) and the quadratic quotient.
4. If possible, factor the quadratic.

How many zeros does a third degree polynomial have?

Third-degree polynomials can have 3 possible zeros due to: – Because the degree of the polynomial indicates the number of zeros in an…

How many solutions does a 3rd degree polynomial have?

That means the third root must be a real number, because each complex number can only have 1 complex conjugate. In other words, P(x) must cross the x-axis either once (1 real root and 2 complex roots), or 3 times (3 real roots). A third degree polynomial has three solutions, which may be real or complex.

How many X-intercepts does a 3rd degree polynomial have?

two x-intercepts
The graph of a third degree polynomial f(x) has exactly two x-intercepts.

Can a third degree polynomial have one X intercept?

(Some cubics, however, cannot be factored.) A cubic function may have one, two or three x -intercepts, corresponding to the real roots of the related cubic equation.