Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x2 + bx + c

5.3 – Factoring x2 + bx + c Today we will be learning how to: Factor trinomials of the form x2 + bx + c

5.3 – Factoring x2 + bx + c If all terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor (GCF) When factoring, ALWAYS CHECK FOR A GCF FIRST!!

5.3 – Factoring x2 + bx + c Example 1 Factor out the GCF of: 8y2 + 16y5 6a4 – 8a2 + 2a

5.3 – Factoring x2 + bx + c Example 2 Factor out the GCF of: -15x3y + 9x2y7 -5x2y – x2 + 3x3y5 + 11x7

HOMEWORK 5.3 Part 1 Practice 5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Part 1 Practice

5.3 – Factoring x2 + bx + c We know how to write (x + 3)(x + 5) as x2 + 8x + 15 Now we’re going to learn how to take a trinomial like x2 + 8x + 15 and write it as a product of binomials (x + 3)(x + 5)

5.3 – Factoring x2 + bx + c Factoring Polynomial When… The degree is 2 (quadratic) The number of terms is 3 (trinomial) The coefficient of the squared term is 1 x2 + bx + c b add c multiply

5.3 – Factoring x2 + bx + c Steps to factoring success Draw your parentheses and fill in the variable. In your x-puzzle: b goes in the addition spot and c goes in the multiplication spot. What will your signs need to be? Solve the x-puzzle and put your answer in ( ) Check your work by distributing

5.3 – Factoring x2 + bx + c Example: Factor r2 + 4r + 3 (r )(r ) 4 3 multiply add

5.3 – Factoring x2 + bx + c Example 1 Factor the expression. x2 + 10x + 9 x2 + 8x + 15

5.3 – Factoring x2 + bx + c Example 2 Factor the expression. x2 – 10x + 25 x2 – 2x + 1

5.3 – Factoring x2 + bx + c Example 3 Factor the expression. x2 – 14x + 24 x2 + 6x + 9

5.3 Part 2 Practice Worksheet 5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Part 2 Practice Worksheet

5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Practice A #2 – 4, 6 – 8, 11 – 12, 15, 18

5.3 – Factoring x2 + bx + c Example 1 Factor the expression. x2 – 3x – 18 x2 + 5x – 6

5.3 – Factoring x2 + bx + c Example 2 Factor the expression. x2 – 2x – 35 x2 + 4x – 21

5.3 – Factoring x2 + bx + c Example 3 Factor the expression. x2 + x – 20 x2 – 4x – 5

5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Part 3 Practice

5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Practice B Worksheet #1 – 18