A cubic with roots a, b, c has form:
f(x) = (x - a)(x - b)(x - c)
Thus the cubic with roots 3, -6 and 0 is given by:
f(x) = (x - 3)(x - -6)(x - 0)
→ f(x) = (x - 3)(x + 6)x
→ f(x) = (x² + 3x - 18)x
→ f(x) = x³ + 3x² - 18x
ax2 + bx + c is the standard form for quadratic. ax3 + bx2 + cx + d for cubic etc etc
x3 - 2x2 - 25x + 50 = 0
x3 + 4x2 - 25x - 100 = 0
That already is a polynomial in standard form.
It is x^3 - x^2 - 4x + 4 = 0
ax2 + bx + c is the standard form for quadratic. ax3 + bx2 + cx + d for cubic etc etc
x3 - 2x2 - 25x + 50 = 0
The graph of a cubic polynomial is called a cubic curve. It typically has an "S" shape and can have one, two, or three real roots, depending on the polynomial's coefficients. The general form of a cubic polynomial is ( f(x) = ax^3 + bx^2 + cx + d ), where ( a \neq 0 ). The behavior of the graph includes turning points and can exhibit inflection points where the curvature changes.
x3 + 4x2 - 25x - 100 = 0
Rational roots
That already is a polynomial in standard form.
It is x^3 - x^2 - 4x + 4 = 0
The standard form of a polynomial of degree n is anxn + an-1xn-1 + ... + a1x + a0 where the ai are constants.
A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.
The factored form of a polynomial is valuable because it simplifies the process of finding its roots or zeros, making it easier to solve equations. It also provides insights into the polynomial's behavior, such as identifying multiplicities of roots and understanding its graph. Additionally, factored form can facilitate polynomial division and help in applications such as optimization and modeling in various fields.
Standard Form
A cubic polynomial is a mathematical expression of the form ( f(x) = ax^3 + bx^2 + cx + d ), where ( a, b, c, ) and ( d ) are constants and ( a \neq 0 ). This type of polynomial has a degree of three, meaning its highest exponent is three. Cubic polynomials can have up to three real roots and exhibit a characteristic "S" shaped curve when graphed. They are often used in various fields, including physics and engineering, to model complex relationships.