6 5 Factoring Quadratics with Prime Leading Coefficients

6. 5 Factoring Quadratics with Prime Leading Coefficients Objective: Be able to factor quadratics that start with a prime number.

Example 1 Factor this quadratic: 2 3 x + 11 x + 10 Step one: 3 • 10 = 30 Step two: Find a factor pair of 30 whose sum is 11.

Example 1 Factor this quadratic: 2 3 x + 11 x + 10 30 1 2 3 5 30 15 10 6 31 17 13 11

Example 1 Factor this quadratic: 2 3 x + 11 x + 10 Step three: Template (3 x )(x )

Example 1 Factor this quadratic: 2 3 x + 11 x + 10 Step four: (3 x + 5)(x + 2) Choose values that create the 5 and 6 from step 2.

Example 1 Factor this quadratic: 2 3 x + 11 x + 10 Step five FOIL to check your work: (3 x + 5)(x + 2) 3 x 2 + 6 x + 5 x +10 3 x 2 +11 x +10

Example 2 Factor this quadratic: 2 5 x + 27 x – 18 Step one: 5 • -18 = -90 Step two: Find a factor pair of -90 whose sum is 27.

Example 2 Factor this quadratic: -1 2 5 x + 27 x – 18 1 -2 2 There are more pairs here, but I stopped when -3 I found the one I needed. 3 -90 90 -90 45 -45 30 -30 89 -89 42 -42 27 -27

Example 2 Factor this quadratic: 2 5 x + 27 x – 18 Step three: Template (5 x )(x )

Example 2 Factor this quadratic: 2 5 x + 27 x – 18 Step four: (5 x – 3)(x + 6) Choose values that create the -3 and 30 from step 2.

Example 2 Factor this quadratic: 2 5 x + 27 x – 18 Step five FOIL to check your work: (5 x – 3)(x + 6) 2 5 x + 30 x – 3 x – 18 2 5 x +27 x – 18

Assignment 6. 5 Worksheet