Lesson 6 5 Factoring ax 2 bx c

Lesson 6 -5 Factoring ax 2 + bx + c Standard 11. 0 Apply basic factoring techniques to second degree polynomials Taken from: Rebecca Renken, Mathematics Department, Francis Howell High School

Example 1 • Factor 17 x + 10 + 3 x 2 • Before factoring a trinomial it must be written in descending order • You must always look for the greatest common factor first…it may be a negative. • The coefficient of the squared term must be positive. • If the coefficient of the squared term is greater than one that is what tells you to use the box and diamond method

Example 1 Solution Box and Diamond Method • Factor 17 x + 10 + 3 x 2 + 17 x + 10, no greatest common factor • Draw a box put the first and last term diagonal from each other • Then multiply the coefficients together and this will give you the number for the north 3 x 2 10

Example 1 Solution Box and Diamond Method 3 x 2 + 17 x + 10 3 x 2∙ 10 = 30 x 2 What can you multiply to get 30 that adds up to 17? 30 3 x 2 10 17 The coefficient of the middle term is in the south

Example 1 Solution Box and Diamond Method 3 x 2 + 17 x + 10 3 x 2∙ 10 = 30 x 2 What can you multiply to get 30 that adds up to 17? Put those same two terms in your box multiplied by the variable 30 3 x 2 2 15 10 17

Example 1 Solution Box and Diamond Method 3 x 2 + 17 x + 10 Now factor out the greatest common factor from each row and column The signs from your diamond apply to the box 3 x 2 15 x 2 x 10 30 2 15 17

Example 1 Solution Box and Diamond Method 3 x 2 + 17 x + 10 Now factor out the greatest common factor from each row and column The signs from your diamond apply to the box 3 x +2 x +5 3 x 2 15 x 2 x 10 30 2 15 The answer is (3 x + 2)(x + 5) 17

Example 2 • Factor 12 x 2 + x - 6

Example 2 • Factor 12 x 2 + x – 6 3 x 4 x +3 12 x 2 9 x -2 -8 x -6 • The answer is (4 x + 3)(3 x – 2) -72 -8 9 1

Example 3 • Factor 30 x 2 -23 x +3 • The answer is

Example 3 • Factor 30 x 2 -23 x +3 5 x 6 x -1 30 x 2 -5 x -3 -18 x 3 • The answer is (6 x - 1)(5 x – 3) 90 -5 -18 -23

Things to Remember • Always check for the GCF…it might be negative. • The signs of the numbers in the “west” and “east” indicate the signs that must be in your parentheses. • Check your work by using the FOIL method.

Burning Questions? ?