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5.4 – Factoring ax 2 + bx + c

5.4 – Factoring ax 2 + bx + c. When you have x 2 + bx + c, to factor it, we found the factors of the constant that added to the middle term But, when you have ax 2 + bx + c, things become a little more tricky We will still use a similar method. Factoring ax 2 + bx + c.

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5.4 – Factoring ax 2 + bx + c

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  1. 5.4 – Factoring ax2 + bx + c

  2. When you have x2 + bx + c, to factor it, we found the factors of the constant that added to the middle term • But, when you have ax2 + bx + c, things become a little more tricky • We will still use a similar method

  3. Factoring ax2 + bx + c • We will have to take into account the leading coefficient a, when a is not 1 • Example. Factor 2x2 + 3x - 5 • New Method: • 1) Multiply a and c together

  4. 2) Find the factors of a(c) that add to the middle term • a(c) = • Factors that add to 3?

  5. 3) “Split” the middle term as each factor • Split 3 as…

  6. 4) Group together the first two, and last two terms • Find any common factors they share

  7. 5) Pull out the “common binomial” • Should always be the same binomial

  8. 6) Write the second binomial as the common factors

  9. Rule of Thumb • When you factor these, you will always have a common binomial, and a second binomial made up of the common factors • If you do not get back to the common binomial, double check your signs or the GCF you pulled out

  10. Example. Factor 5x2 + 8x + 3

  11. Example. Factor 5x2 + 13x + 6

  12. Example. Factor 3x2 + 9x + 6

  13. Example. Factor 5z2 + 25z - 70

  14. Assignment • Pg. 244 • 3-9, 21-37 odd

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