4.4A Factoring: Leading Coefficient ≠1

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Presentation transcript:

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

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 ( - )( - )

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

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

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

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 𝑋 2 ( ) : 0 is a solution twice X³( ) : 0 is a solution 3 times #( ) : No solution comes form the # out front

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