2.6 Factor x2 + bx + c provided ________ = b and ______ = c FACTORING x2 + bx + c Algebra provided ________ = b and ______ = c Example because ________ = 6 and ______ = 5

2.6 Factor x2 + bx + c Factor when b and c are positive Solution Example 1 Factor when b and c are positive Solution Find two ________ factors of ___ whose sum is ____. positive 16 10 Make an organized list. Factors of _____ Sum of factors 16, ___ 16 + ___ = ____ 8, ___ 8 + ___ = ____ 4, ___ 4 + ___ = ____ The factors of 8 and ___ have a sum of ___, so they are the correct values of p and q. 2 10

2.6 Factor x2 + bx + c Factor when b and c are positive Check Example 1 Factor when b and c are positive Check Multiply. Simplify.

2.6 Factor x2 + bx + c Factor when b is negative and c is positive Example 2 Factor when b is negative and c is positive Solution Because b is negative and c is positive, p and q must __________. be negative Factors of _____ Sum of factors ____, ____ ___ +( ___) = ____ ____, ____ ___ +( ___) = ____

2.6 Factor x2 + bx + c Factor when b is positive and c is negative Example 3 Factor when b is positive and c is negative Solution Because c is negative, p and q must __________________. have different signs Factors of _____ Sum of factors -10, ____ -10 + ____= ___ 10, ____ 10 + ____= ___ -5, ____ -5 + ____= ___ 5, ____ 5 + ____= ___

2.6 Factor x2 + bx + c Checkpoint. Factor the trinomial.

2.6 Factor x2 + bx + c Solve a polynomial equation 18 x = ______ Example 4 Solve a polynomial equation Solve the equation Write original equation. Subtract _____ from each side. 18 Factor left side. Zero-product property. x = ______ or x = _____ Solve for x. -9 and 2 The solutions of the equation are ______________.

2.6 Factor x2 + bx + c Checkpoint. Complete the following exercise. 7. Solve the equation

2.6 Factor x2 + bx + c