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# Math 11

### SLS - Math 11 - Ch 4- Quadratic & Polynomial Equations

Question | Definition |
---|---|

Remainder Theorem | When a polynomial P(x) is divided by x-b, the remainder is P(b). ie, replace x with b and simplify. |

Factor Theorem | When x-b is a factor of the polynomial P(x), P(b)=0 |

The discriminant of a quadratic equation is negative in this case | When there are no real solutions (only imaginary solutions). |

The discriminant of a quadratic equation is zero in this case | When there are two equal real solutions (looks like one solution). |

The discriminant of a quadratic equation is positive in this case | When there are two distinct real solutions. |

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 |

Describe how to solve a quadratic by graphing. | Move all terms to one side. Input in calculator. Find x intercepts. |

Two other names for a "root" of a quadratic equation are: | Any 2 of: zero of the graph, x intercept of the graph, solution |

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. |

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. |

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. |

List three types of polynomials by degree. | Any 3 of: Linear, Quadratic, Cubic, Quartic, Quintic. |

List 2 types of polynomials by number of terms. | Any three of: monomial, binomial, trinomial (and the general description polynomial) |

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. |

Describe the graphical method to solve a polynomial equation (other than a quadratic). | Move all terms to one side. Graph and find the zeros. |

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. |

Created by:
slscarrie