Quadratic Polynomials by: Kameron Falls

what is a quadratic polynomial A quadratic polynomail is a polynomial of degree 2. A univariate quadratic polynomial has the form. An equation involving a quadratic polynomial is called a quadratic equation. A closed-form solution known as the quadratic formula exists for the solutions of an arbitrary quadratic equation.

Here are examples of quadratic equations in the standard form (ax² + bx + c = 0): 6x² + 11x – 35 = 0 2x² – 4x – 2 = 0 -4x² – 7x +12 = 0

Here are examples of quadratic equations lacking the linear coefficient or the “bx”: 2x² – 64 = 0 x² – 16 = 0 9x² + 49 = 0

Here are examples of quadratic equations lacking the constant term or “c”: x² – 7x = 0 2x² + 8 -x² – 9x = 0

Here are examples of quadratic equation in factored form (x + 2)(x – 3) = 0 [upon computing becomes x² -1x – 6 = 0] (x + 1)(x + 6) = 0 [upon computing becomes x² + 7x + 6 = 0] (x – 6)(x + 1) = 0 [upon computing becomes x² – 5x – 6 = 0]

pictures of quadratic function

synthetic division Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

synthetic division If you are given, say, the polynomial equation y =x 2 + 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2). Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x = –2 and x = –3 are the two zeroes of y.

synthetic division example

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