4.3 “Solve x2 + bx + c by Factoring”Vocabulary to Know: • Monomial

• Binomial

• Trinomial

• Roots of a Function

• Zeros of a Function

Use FOIL to multiply the two binomials…

(x + 4)(x – 7)

Factoring is sort of like reverse FOIL.

Examples: Factor the following:

1. x2 – 9x + 20

2. x2 – 3x – 18

3. r2 + 2r – 63

4. x2 + 14x + 48

More Examples: 5. x2 + 3x – 12

6. m2 – 17m + 72

7. y2 – 4y – 60

8. x2 – x – 42

Special Pattern: Difference of Two Squares:**These are binomials only**

a2 – b2 = (a + b)(a – b)

For example….

1. x2 – 25

2. x2 – 100

3. y2 – 64

4. m2 – 49

Try These: 1. x2 – 4x – 12

2. m2 + m + 72

3. k2 + 2k - 24

4. y2 – 7y – 60

5. x2 – 225

6. p2 – 15p + 50

Find the Roots of the Equations: These problems will have an equal sign and may say…Find zeros, roots, solutions…it means the same thing, where the quadratic hits the x-axis.

Examples:

1. x2 – x – 42 = 0

2. f(x) = x2 -10x + 25

3. y = x2 – 7x – 30

4. y2 = 5y

Word Problem1. You are placing a stone border along two sides of a rectangular garden that measures 9 yards by 12 yards. Your budget limits you to only enough stone to cover 72 yards. How wide should the border be?

Another Word Problem2. Julie is making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?