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Chapter 5 – Quadratic Functions and Factoring

Chapter 5 – Quadratic Functions and Factoring. 5.3 – Factoring x 2 + bx + c. 5.3 – Factoring x 2 + bx + c. Today we will be learning how to: Factor trinomials of the form x 2 + bx + c. 5.3 – Factoring x 2 + bx + c.

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Chapter 5 – Quadratic Functions and Factoring

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

  2. 5.3 – Factoring x2 + bx + c • Today we will be learning how to: • Factor trinomials of the form x2 + bx + c

  3. 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

  4. 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. 5.3 – Factoring x2 + bx + c • Example 1 Factor the expression. • x2 + 14x + 48 • x2 – x – 6

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

  7. 5.3 – Factoring x2 + bx + c • 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.

  8. 5.3 – Factoring x2 + bx + c • Example 3 Solve the equations. • x2 – x = 42 • x2 + 10x = -16

  9. 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.

  10. 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?

  11. 5.3 – Factoring x2 + bx + c Classwork 5.3 Worksheet Odd Problems

  12. 5.3 – Factoring x2 + bx + c Homework 5.3 Worksheet Even Problems

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