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Factoring Trinomials with a > 1

Factoring Trinomials with a > 1. Factor trinomials when the coefficient of x 2 is a number greater than 1. a x 2 + b x + c. Multiply 3 times 6. 3x 2 + 11x + 6 18 + 11 1 • 18 2 • 9. product sum. To make the sum positive, both numbers must be positive.

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Factoring Trinomials with a > 1

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  1. Factoring Trinomials with a > 1 Factor trinomials when the coefficient of x2 is a number greater than 1. ax 2 + bx + c

  2. Multiply 3 times 6. 3x 2 + 11x + 6 18 + 11 1 • 18 2 • 9 product sum To make the sum positive, both numbers must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x + 9 ) + 19 + 11 Check using the F.O.I.L. method: ( 3x + 2 ) ( x + 3 ) 3x 2 + 9x + 2x + 6 3x 2 + 11x + 6 1 1 3 3 ( x + 3 ) ( 3x + 2 )

  3. Multiply 3 times – 6. 3x 2 + 7x – 6 –18 + 7 –1 • 18 –2 • 9 product sum To make the sum positive, the largest number must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x – 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x – 2 ) ( 3x + 9 ) + 17 + 7 Check using the F.O.I.L. method: ( 3x – 2 ) ( x + 3 ) 3x 2 + 9x – 2x – 6 3x 2 + 7x – 6 1 1 3 3 ( x + 3 ) ( 3x – 2 )

  4. Multiply 3 times – 6. 3x 2– 7x – 6 –18 – 7 1 • –18 2 • – 9 product sum To make the sum negative, the largest number must be negative. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x – 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x – 9 ) – 17 – 7 Check using the F.O.I.L. method: ( 3x + 2 ) ( x – 3 ) 3x 2– 9x + 2x – 6 3x 2– 7x – 6 1 1 3 3 ( x – 3 ) ( 3x + 2 )

  5. Multiply 9 times 4. 9x 2– 12x + 4 36– 12 –1 • –36 –2 • –18 –3 • –12 –4 • –9 –6 • –6 Use the coefficient of x 2 in both parentheses: ( 9x ) ( 9x ) Fill in the numbers… ( 9x – 6 ) ( 9x – 6 ) Factor any common terms from each parenthesis. ( 9x – 6 ) ( 9x – 6 ) product sum To make the sum negative, both numbers must be negative. – 37 – 20 – 15 – 13 – 12 Check using the F.O.I.L. method: ( 3x – 2 ) ( 3x – 2 ) 9x 2– 6x – 6x + 4 9x 2– 12x + 4 3 3 3 3 ( 3x – 2 ) ( 3x – 2 ) ( 3x – 2 ) 2

  6. Multiply – 9 times 4. 4x 2– 9 – 36 0 1 • – 36 6 • – 6 Use the coefficient of x 2 in both parentheses: ( 4x ) ( 4x ) Fill in the numbers… ( 4x + 6 ) ( 4x – 6 ) Factor any common terms from each parenthesis. ( 4x + 6 ) ( 4x – 6 ) product sum To make the sum zero, both numbers must be the same but opposite signs. – 35 0 Check using the F.O.I.L. method: ( 2x + 3 ) ( 2x – 3 ) 4x 2– 6x + 6x – 9 4x 2– 9 2 2 2 2 ( 2x – 3 ) ( 2x + 3 )

  7. ALWAYS check your work when factoring trinomials by using the FOIL method.

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