Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x2 + bx + c

5.3 – Factoring x2 + bx + c Today we will be learning how to: Factor trinomials of the form x2 + bx + c

5.3 – Factoring x2 + bx + c We know how to write (x + 3)(x + 5) as x2 + 8x + 15 x + 3 and x + 5 are binomials Trinomial – sum of three monomials

5.3 – Factoring x2 + bx + c We can factor to write a trinomial was the product of two binomials. To write x2 + bx + c as (x + m)(x + n), look at the pattern: (x + m)(x + n) = x2 + nx + mx + mn = x2 + (m + n)x + mn In order to factor x2 + bx + c, we must find integers m and n such that m + n = b and mn = c

5.3 – Factoring x2 + bx + c Example 1 Factor the expression. x2 + 14x + 48 x2 – x – 6

5.3 – Factoring x2 + bx + c Example 2 Factor the expression. x2 + 6x – 7 x2 – x – 6

5.3 – Factoring x2 + bx + c Zero Product Property We can use factoring to solve some quadratic equations (ax2 + bx + c = 0) Zero Product Property When the product of two expressions is zero, then at least one of the expressions must equal zero. Let A and B be expressions. If AB = 0, then A = 0 or B = 0. If (x + 5)(x + 2) = 0, then x + 5 = 0 or x + 2 = 0.

5.3 – Factoring x2 + bx + c Example 3 Solve the equations. x2 – x = 42

5.3 – Factoring x2 + bx + c Example 4 Your school plans to increase the area of the parking lot by 1000 square yards. The original parking lot is a rectangle. The length and the width of the parking lot will each increase by x yards. The width of the original parking lot is 40 yards, and the length of the original parking lot is 50 yards.

5.3 – Factoring x2 + bx + c Example 4 – continued Find the area of the original parking lot. Find the total area of the parking lot with the new space. Write an equation that you can use to find the value of x. Solve the equation. How many yards should the length and width of the parking lot increase?

5.3 – Factoring x2 + bx + c Classwork 5.3 Worksheet Odd Problems

5.3 – Factoring x2 + bx + c Homework 5.3 Worksheet Even Problems