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Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x 2 + bx + c.

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Presentation on theme: "Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x 2 + bx + c."— Presentation transcript:

1 Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x 2 + bx + c

2 Today we will be learning how to:  Factor trinomials of the form x 2 + bx + c

3 5.3 – Factoring x 2 + bx + c We know how to write (x + 3)(x + 5) as x 2 + 8x + 15 x + 3 and x + 5 are binomials Trinomial – sum of three monomials

4 5.3 – Factoring x 2 + bx + c We can factor to write a trinomial was the product of two binomials. To write x 2 + bx + c as (x + m)(x + n), look at the pattern: (x + m)(x + n) = x 2 + nx + mx + mn = x 2 + (m + n)x + mn  In order to factor x 2 + bx + c, we must find integers m and n such that m + n = b and mn = c

5 5.3 – Factoring x 2 + bx + c Example 1 Factor the expression.  x x + 48  x 2 – x – 6

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

7 5.3 – Factoring x 2 + bx + c We can use factoring to solve some quadratic equations (ax 2 + 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.

8 5.3 – Factoring x 2 + bx + c Example 3 Solve the equations.  x 2 – x = 42  x x = -16

9 5.3 – Factoring x 2 + 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.

10 5.3 – Factoring x 2 + 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?

11 5.3 – Factoring x 2 + bx + c Classwork 5.3 Worksheet Odd Problems

12 5.3 – Factoring x 2 + bx + c Homework 5.3 Worksheet Even Problems


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