SLS - Math 11 - Ch 4- Quadratic & Polynomial Equations
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Remainder Theorem | When a polynomial P(x) is divided by x-b, the remainder is P(b). ie, replace x with b and simplify.
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| Factor Theorem | When x-b is a factor of the polynomial P(x), P(b)=0
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| The discriminant of a quadratic equation is negative in this case | When there are no real solutions (only imaginary solutions).
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| The discriminant of a quadratic equation is zero in this case | When there are two equal real solutions (looks like one solution).
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| The discriminant of a quadratic equation is positive in this case | When there are two distinct real solutions.
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| What are 3 methods of solving a quadratic equation? | any 3 of: graphing,
factoring,
the square root principle,
the quadratic formula,
or completing the square
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| Describe how to solve a quadratic by graphing. | Move all terms to one side. Input in calculator. Find x intercepts.
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| Two other names for a "root" of a quadratic equation are: | Any 2 of:
zero of the graph,
x intercept of the graph,
solution
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| Describe how to solve a quadratic by factoring. | Move all terms to one side, simplify and write in descending order. Factor. If factors are (2x-5)(x+4) the solutions are 5/2 and -4.
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| Describe how to solve a quadratic with the square root principle. | There must be an x^2 term and a constant. No x term or other terms. Move the x^2 term to one side and the constant to the other. Square root both sides, with +- on the root. Reduce the radical. Isolate x.
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| Describe how to solve a quadratic with the quadratic formula. | Move all terms to one side, simplify and write in descending order. Plug coefficients into the quadratic formula. Simplify the positive and negative answers separately.
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| List three types of polynomials by degree. | Any 3 of: Linear, Quadratic, Cubic, Quartic, Quintic.
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| List 2 types of polynomials by number of terms. | Any three of: monomial, binomial, trinomial (and the general description polynomial)
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| The Rational Zero Theorem | The possible rational zeros of a polynomial are the factors of the constant term divided by the factors of the leading coefficient.
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| Describe the graphical method to solve a polynomial equation (other than a quadratic). | Move all terms to one side. Graph and find the zeros.
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| Describe the algebraic method for solving a polynomial of degree 3 or more. | Use the rational root theorem, factor theorem, and synthetic division until a quadratic remains. Factor it.
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