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Section 9-5 Factoring Trinomials

Section 9-5 Factoring Trinomials. x 2 + bx + c Day Two. Sign Rules for “—’’ c term. ( + – ) ( + )( – ) ( – – ) ( + )( – ). The factors of the last term SUBTRACT to be the middle term. The LARGER factor goes with the sign of the middle term.

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Section 9-5 Factoring Trinomials

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  1. Section 9-5Factoring Trinomials x2 + bx + c Day Two

  2. Sign Rules for “—’’ c term • ( + – ) ( + )( – ) • ( – – ) ( + )( – ) • The factors of the last term SUBTRACT to be the middle term. • TheLARGERfactor goes with the signof the middleterm.

  3. Example 1 Factors of the last term: a2 – a – 30 30 1 and 30 2 and 15 ( )( ) a + 5 a – 6 3 and 10 Using the Sign Rules – What are the signs for this trinomial? 5 and 6 Which set subtracts to be 1? 5 and 6 The larger factor goes with the sign of the middle term. 1 plus sign & 1 minus sign

  4. Example 2 Factors of the last term: 64 x2 + 12x – 64 1 and 64 2 and 32 4 ( )( ) x + 16 x - 4 and 16 8 and 8 Using the Sign Rules – What are the signs for this trinomial? Which set subtracts to be 12? 4 and 16 The larger factor goes with the sign of the middle term. 1 plus sign 1 minus sign

  5. Example 3 Factors of the last term: Find the zeros: f(x) = x2 + 7x – 8 8 1 and 8 2 and 4 ( )( ) = 0 x + 8 x – 1 Which set subtracts to be 7? Using the Sign Rules – What are the signs for this trinomial? 1 and 8 The larger factor goes with the sign of the middle term. 1 plus sign 1 minus sign Solve: x + 8 = 0 and x – 1 = 0 x = -8 and x = 1

  6. Example 4 Factors of the last term: x2 – 3xy – 10y2 10 1 and 10 2 and 5 ( )( ) x + 2y x - 5y Which set subtracts to be 3? Using the Sign Rules – What are the signs for this trinomial? 2 and 5 The larger factor goes with the sign of the middle term. 1 plus sign 1 minus sign

  7. Homework 9.5 Day 2 Pg 586-587 7, 9, 11, 12, 13, 16, 21, 24, 34, 35, 36, 51

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