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4.4A Factoring: Leading Coefficient ≠1

4.4A Factoring: Leading Coefficient ≠1. Factoring Difference of 2 Squares LC ≠ 1 2 terms SUBTRACTION Both have NICE Square roots Put square roots of each in the ( ) ( + )( - ) : Use one of each sign. Examples: Difference of 2 squares: LC ≠1. 1. 16x² - 1 2. 36x² - 9

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4.4A Factoring: Leading Coefficient ≠1

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  1. 4.4A Factoring: Leading Coefficient ≠1 • Factoring Difference of 2 Squares LC≠ 1 • 2 terms • SUBTRACTION • Both have NICE Square roots • Put square roots of each in the ( ) • ( + )( - ) : Use one of each sign

  2. Examples: Difference of 2 squares: LC ≠1 • 1. 16x² - 1 • 2. 36x² - 9 • 3. 9x² - 64

  3. Factoring Perfect Square Trinomials: Leading Coefficient ≠1 • Factoring Perfect Square Trinomials: LC≠1 • 3 terms • LAST term is POSITIVE • FIRST AND LAST have NICE square roots • Put square root of first & last in ( ) • BOTH signs MATCH sign of MIDDLE term (SAME) • Check by FOIL • ( + )( + ) OR ( - )( - )

  4. Examples: Perfect Square Trinomial: LC ≠1 • 4. 4x² + 20x + 25 • 5. 36x² - 12x + 1 • 6. 9x² + 12x + 4 • 7. 25x² - 80x + 64

  5. Factorable Trinomial LC≠1: Guess & Check by FOIL • Trinomial: FIRST MIDDLELAST • (____ ) (____ ) • 2 things multiplied = first • ( ___) ( ___) • 2 things multiplied = last • (___ ___) (____ ____) “O + I” = Middle • LAST= POSITIVE: ( + )( + ) OR ( - ) ( - ) match middle • LAST = NEGATIVE: ( + ) ( - ) one of each

  6. Examples: Factorable LC≠1 • 8. 2x²+ 7x + 3 • 9. 5x² -11x +6 • 10. 5x² + 16x + 3 • 11. 4x² - 9x + 2 • 12. 3x² + 5x -12 • 13. 7x² - 20x -3 • 14. 15x² - 2x -8 • 15. 11x² + 2x -9

  7. Solving quadratics: (Find x-intercepts, zeros, roots, solutions) • FACTOR first • Solve EACH factor • (x #) : use OPPOSITE of number in ( ) • (#x #) : set ( ) = 0 and solve for x • X( ) : One solution is 0 • ( ) : 0 is a solution twice • X³( ) : 0 is a solution 3 times • #( ) : No solution comes form the # out front

  8. Examples: Solve • 16. 9x² - 13x – 10 = 0 • 17. y = 2x² + 5x + 3

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