WARM UP

• Find the product.

• 1.) (m – 8)(m – 9)

• 2.) (z + 6)(z – 10)

• 3.) (y + 20)(y – 20)

Algebra II

4.3 SOLVE X2 + BX + C = 0 BY FACTORING

OBJECTIVE• Solve quadratic equations.

VOCABULARY

• Monomial – an expression that is either a number, a variable, or the product of a number and one or more variables.

• Binomial – sum of two monomials.

• Trinomial – sum of three monomials.

EXAMPLE 1 – FACTOR TRINOMIALS IN THE FORM AX2 + BX + C = 0

• Factor the expression.

• A.) x2 + 14x + 48

• B.) x2 – 9x - 5

SPECIAL FACTORING PATTERNS

• Difference of two squares pattern

• a2 – b2 = (a + b)(a – b)

• Example: x2 – 4 = (x +2)(x – 2)

SPECIAL FACTORING PATTERNS CONTINUED

• Perfect Square Trinomial

• a2 + 2ab + b2 = (a + b)2

• Example: x2 + 6x + 9 = (x +3)2

• a2 – 2ab + b2 = (a – b)2

• Example: x2 – 4x + 4 = (x – 2)2

EXAMPLE 2 – FACTOR WITH SPECIAL PATTERNS

• Factor the expression.

• A.) m2 – 121

• B.) r2 + 14r + 49

• C.) p2 – 24p + 144

WARM UP

• Find the product.

• A.) (d + 9)2

• B.) (x – 14)2

• Factor the expression.

• C.) x2 – 9x + 20

ZERO PRODUCT PROPERTY

• If the product of two expressions is zero, then one or both of the expressions equal zero.

• Example: If (x + 5)(x + 2) = 0, then x + 5 = 0 or x + 2 = 0. That is, x = -5 or x = -2.

EXAMPLE 3

• What are the roots of the equation x2 – x – 42 = 0?

EXAMPLE 5 – FIND THE ZEROS OF THE QUADRATIC FUNCTIONS

• Find the zeros of the function by rewriting the function in intercept form.

• y = x2 + 3x - 28

ASSIGNMENT

• Pg. 255 – 256 (10 – 32 even)