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Basic Math/Algebra II (Polynomials)

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Expert: Josh - 5/6/2004


Question
i have a major test comming up that may decide if i graduate or not and i don't know how to do half of it please help!

Wrtie a polynomial whose graph has the given x-intercepts and has a leading coefficient of 1
(-1,0),(2,0),(-3,0)

Answer
Mandi,

You cannot leave things till the last minute. If anything, preparation for the exam should be an ongoing process which starts from day 1.

If the points x=-1,2,-3 represent the x-axis intercepts, meaning that the expression has a corresponding y-value of zero at these points, then, these are the zeros (i.e., the solutions) to the polynomial.

Factorize them as follows:
(x+1)(x-2)(x+3)=0
Reason for doing this is because x=-1,2,-3 are solutions to the polynomial by definition, as you can readily check.

You can then expand this, if you wish, to get
(x+1)(x-2)(x+3)=0
(x^2-x-2)(x+3)=0
(x^3+2x^2-5x-6)=0

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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