Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 1 of 6 Attendance Problems. Find each product. 1.(x – 2)(2x + 7) 2. (3y + 4)(2y + 9) 3. (3n – 5)(n – 7) Factor each trinomial. 4. x2 +4x – 32 5. z2 + 15z + 36 6. h2 – 17h + 72 • I can factor quadratic trinomials of the form ax 2 + bx + c. • I can use a graphing calculator to factor a polynomial by studying its graph. Common Core CC.9-12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4–y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2) (x2 + y2). CC.9-12.A.SSE.3(a) Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. In the previous lesson you factored trinomials of the form x2 + bx + c. Now you will factor trinomials of the form ax2 + bx + c, where a ≠ 0. Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 2 of 6 When you multiply (3x + 2)(2x + 5), the coefficient of the x2-term is the product of the coefficients of the x-terms. Also, the constant term in the trinomial is the product of the constants in the binomials. (3x + 2)(2x + 5) = 6x2 + 19x + 10 Video Example 1: Factor 6x2 + 19x + 10. Guided Practice: 7. Factor 6x2 + 11x + 3 Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 3 of 6 Bob Shueh method to factor (with a leading coefficient.) 1. 2. 3. 4. 5. Write the polynomial in standard form. Use the distributive property to factor out a GCF. Copy the first and last terms. Multiply the first & last coefficients. Use this product in your “diamond.” Rewrite the middle terms using the new diamond. If the two factors have opposite signs, write the negative sign first. 6. Factor by grouping. 8. 3x2 – 2x – 8 Video Example 2: Factor. A. 3x2 + 29x + 18 B. 7x 2 + 17x + 6 Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 4 of 6 Remember! When b is negative and c is positive, the factors of c are both negative. Guided Practice: Factor the following. 9. 6x2 + 17x + 5 11. 3x2 + 13x + 12 10. 9x2 – 15x + 4 Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 5 of 6 Video Example 3: Factor the following: A) 2x2 + 5x – 3 B) 3x2 - 10x – 8 Guided Practice: Factor each trinomial. 11.6x2 + 7x – 3 12. 4n2 – n – 3 When the leading coefficient is negative, factor out –1 from each term before using other factoring methods. Caution When you factor out –1 in an early step, you must carry it through the rest of the steps. Algebra 7-4 Study Guide: Factoring ax 2 + bx + c (pp 480-483 & 487) Page 6 of 6 Video Example 4: Factor –5x2 – 11x – 2 Guided Practice: Factor the following. 13. –6x2 – 17x – 12 14. –3x2 – 17x – 10 7-4 Assignment: (pp 484-485) 30, 35, 48, 50, 54, 58, 64, 65, 70-76.

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