Unit 2 : Factoring
By : Mrinal Bhavsar
Summary of the Unit
What is it?
The factored form of a quadratic equation is y = a (x - r) (x - s)
- The value of a gives you the shape of the graph and the direction of opening
- The value of r and s give you the two x - intercepts (r , 0) and (s , 0)
- To find the y - intercept (0 , y) set x = 0 and solve for y
- To find the vertex use the zeroes to find the axis of symmetry and sub the x value into the given equation to solve for y
Solving a quadratic equation by factoring requires you to take a standard form equation and to factor it. It is called factoring because you find the common factors of the numbers in the equation. When factoring look for Greatest Common Factors or Special Cases. The purpose of using factoring is to be able to break down trinomials and to find the x - intercepts so the equation can be graphed as a parabola.
Factoring can be done in various ways including:
- Multiplying Polynomials
ex : (x + 5) (x - 4)
= x² - 4x + 5x - 20
= x² + x - 20
- Special Products
ex : (x + 3)²
= (x + 3) (x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
- Common Factors
ex : 14m + 12n
= 7 (2m + 3n)
- Factoring Quadratic Expressions of the Form x² + bx + c
ex : x² + 8x + 15
= x² + 3x + 5x + 15
= x (x + 3) + 5 (x + 3)
= (x + 5) (x + 3)
- Factoring Quadratic Expressions of the Form ax² + bx + c
ex : 6x² + 11x + 3
= 6x² + 9x + 2x + 3
= 3x (2x + 3) + (2x + 3)
= (3x+1) (2x + 3)
- Factoring a Perfect Square Trinomial and a Difference of Squares
ex : x² - 36
= x² - 6x + 6x - 36
= (x + 6) (x - 6)