6.5 Factoring Quadratics with Prime Leading Coefficients

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There is a pattern for factoring trinomials of this form, when c

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Presentation transcript:

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: 3x2 + 11x + 10 Step one: 3 • 10 = 30 Step two: Find a factor pair of 30 whose sum is 11.

30 1 30 2 15 3 10 5 6 3x2 + 11x + 10 Example 1 Factor this quadratic: 1 30 2 15 3 10 5 6 31 17 13 11

3x2 + 11x + 10 (3x )(x ) Example 1 Factor this quadratic: Step three: Template (3x )(x )

3x2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 Factor this quadratic: Step four: (3x )(x ) Choose values that create the 5 and 6 from step 2. + 5 + 2

3x2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 3x2 + 6x + 5x +10 Factor this quadratic: 3x2 + 11x + 10 Step five FOIL to check your work: (3x )(x ) 3x2 + 6x + 5x +10 3x2 +11x +10 + 5 + 2

Example 2 Factor this quadratic: 5x2 + 27x – 18 Step one: 5 • -18 = -90 Step two: Find a factor pair of -90 whose sum is 27.

Example 2 -90 -1 90 1 -90 -2 45 2 -45 -3 30 3 -30 Factor this quadratic: 5x2 + 27x – 18 89 -89 42 -42 There are more pairs here, but I stopped when I found the one I needed. 27 -27

5x2 + 27x – 18 (5x )(x ) Example 2 Factor this quadratic: Step three: Template (5x )(x )

5x2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 Factor this quadratic: Step four: (5x )(x ) Choose values that create the -3 and 30 from step 2. – 3 + 6

5x2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 5x2 + 30x – 3x – 18 Factor this quadratic: 5x2 + 27x – 18 Step five FOIL to check your work: (5x )(x ) 5x2 + 30x – 3x – 18 5x2 +27x – 18 – 3 + 6

Assignment 6.5 Worksheet