Factoring Pattern for x2 + bx + c, c positive Chapter 5 Section 5.7

Objective Students will factor quadratic trinomials whose quadratic coefficient is 1 and whose constant term is positive.

Concept In this lesson you will study trinomials that can be factored as a product of the form (x + r)(x + s), where r and s are both positive or both negative.

Concept The product (x + r)(x +s) and the trinomial x2 + (r + s)x + rs represent the same thing. Notice that the coefficient of the x-term is the sum of r and s, and the constant term is the product of r and s.

Example (x + 3)(x + 5) (x – 6)(x – 4)

x2 + bx + c (x + r)(x +s) x2 – bx + c (x – r)(x – s) Concept x2 + bx + c (x + r)(x +s) x2 – bx + c (x – r)(x – s)

Concept The following method will help you factor quadratic trinomials into two sets of parenthesis: 1. List the pairs of factors whose products equal the constant term 2. Find the pair of factors in the list whose sum equals the coefficient of the linear term

Example x2 + 14x + 40

Example y2 – 11y + 18

Example x2 – 10x + 14

Questions

Assignment Worksheet