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

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

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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

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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

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

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

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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.

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

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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.

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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?

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

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

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