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3.1 – Factoring x^2+bx+c

Objectives

  • Define and write the general form of a quadratic trinomial.
  • Find the binomial factors of a quadratic trinomial with a leading coefficient of 1.
  • Determine the signs of a trinomial’s factors based on the sign of its x-term and its constant.

 

Key Terms

  • Binomial – A polynomial with exactly two terms.
  • Constant Term – The term in a polynomial that does not have a variable. The constant term has a degree of zero.
  • Degree – The value of the greatest exponent in a polynomial.
    • ex. 7x^4-x^3+5x-9 is a 4th degree polynomial
  • Factor – To write a number or expression as a product of two or more numbers or expressions. A number or expression that is multiplied by another number or expression.
    • The factors of a quadratic trinomial are two binomials
  • FOIL – A method of multiplying binomials. FOIL stands for First, Outer, Inner, Last, the order in which you would multiply a binomial’s terms.
  • Leading Coefficient – The number multiplied by the variable in the first term in a polynomial.
  • Parabola – The set of points in a plane that are related to a given point (the focus) and a given line (the directrix) by this relationship: the distance from any point on the parabola to the focus is the same as the distance from that point to the directrix.
    • A parabola is a conic section
  • Polynomial – An algebraic expression with one or more terms. None of the variables is in the denominator of a fraction, and any exponents are whole numbers.
  • Quadratic Function – A function that has a degree of 2.
  • Quadratic Trinomial – A polynomial that has exactly three terms and a degree of 2.
  • Trinomial – A polynomial that has exactly three terms.

 

Notes

Quadratic Functions Chart
Alg2A 3.01 - Trinomials


Alg2A 3.01 - FOIL Rules

  • Quadratic functions come in one of the following forms
    • y=ax^2+bx+c
    • x=ay^2+by+c

 

  • Examples of quadratic trinomials
    • y=x^2+4y+1
    • y=3x^2+4x-11
    • y=6x^2-2y-8
  • Factoring Review: Binomials
    • Example: 2x + 16
      • Step 1: Decide which integer can be divided out of each term
        • 2x and 16 are both divisible by 2
      • Step 2: Factor out (reverse distribution) the 2
        • 2 (x + 8) is the factorization

  • Factoring Trinomials
    • Example: x^2 is a trinomial if you write it like this: x^2+0x+0
      • Answer: (x + 0)(x + 0)
Rules for Multiplying Binomials
Alg2A 3.01 - Factoring Rules
Signs and Factors
Alg2A 3.01 - FOIL SignsAlg2A 3.01 - FOIL Signs2
Rules for Factoring
Alg2A 3.01 - Factoring02 Alg2A 3.01 - Factoring03 Alg2A 3.01 - Factoring04

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