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12 results for Polynomials in lessons.

1. Lesson Terms, monomials and polynomials Polynomials and Their Properties

   What a term is, which terms are monomials, how binomials, trinomials and polynomials are named, and how to find the degree of a monomial and of a polynomial.

2. Lesson Standard form and types of polynomials Polynomials and Their Properties

   The standard form of a polynomial in x, leading and constant terms, linear, quadratic, cubic and bi-quadratic polynomials, the constant and zero polynomials, and multinomials.

3. Lesson What an algebraic expression is Algebraic Expressions and Their Uses

   Terms combined by the fundamental operations, and how to sort expressions into monomials, binomials, trinomials, polynomials and multinomials by counting terms and checking powers.

4. Lesson Factorising cubics and quartics Polynomials and Their Properties

   Using a given factor or a factor found by trial with the factor theorem to factorise cubic and bi-quadratic polynomials completely.

5. Lesson Dividing algebraic expressions Factorization

   Divide monomials, divide a polynomial by a monomial, divide polynomials by factorising and cancelling, and use long division and the short cut for x minus a number.

6. Lesson The degree of an expression Algebraic Expressions and Their Uses

   The degree of a monomial as the sum of the powers, why a number has degree zero and zero has none, and the degree of a polynomial as its greatest term degree.

7. Lesson Functions and Their Graphs Relations and Functions

   Functions as special relations, the standard real functions with domains and ranges, and the algebra of functions.

8. Lesson Continuity and Differentiability Continuity and Differentiability

   Continuity at a point, piecewise functions, finding constants for continuity, and the link between continuity and differentiability.

9. Lesson Continuity and Differentiability: Mixed Practice, Worked Solutions Continuity and Differentiability

   Step-by-step solutions to every practice question in the lesson “Continuity and Differentiability: Mixed Practice”, with each answer checked.

10. Lesson Value, zeros and roots of a polynomial Polynomials and Their Properties

    Equations by degree, the value p(α) of a polynomial, zeros of a polynomial, roots of an equation, and solving quadratic equations by splitting the middle term.

11. Lesson Long division and the division algorithm Polynomials and Their Properties

    Dividing one polynomial by another step by step, finding the quotient and remainder, and checking the answer with f(x) = g(x)q(x) + r(x).

12. Lesson The remainder theorem Polynomials and Their Properties

    Finding the remainder on division by x − a, ax − b or ax + b without dividing, and using remainders to find unknown coefficients.