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Students will investigate the factorization of x square + bx + c and ax square+bx+c. It is the intent of the project to develop the student` insight into the trinomial factorization process. Here x square +bx+c, where a, b, and c denote constant values and the x term signifies the unknown variable, often can be factored into the product of tow terms. Student will use algebra tiles to indentify the binomial factors. This sets the stage for the students to later learn how to solve polynomial equations and explore relationships between the trinomial x square +bx+c its factored from (x+m) (x+n).

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Navigate the web to search about the definition of the word factor and the use of algebra tiles to factor trinomials. Factor is like talking a number a part. I mean to express a number as the product of its factor. Also factor are either composite number or prime number (except that 0 and 1 are either prime nor composite.

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Polynomial: x square+ bx +cFactors: ( x + m ) ( x + m ) x square+2x+1(x+1) x square+3x+2(x+2) (x+1) x square+7x+6(x+4) (x+3) x square+5x+6(x+3) (x+2) x square+5x+4(x+4) (x+1) 2x square+3x+1(x+1) (x+2) 2x square+7x+3(x+4) (x+3) 3x square+7x+2(x+6) (x+1) 4x square+8x+3(x+6) (x+2)

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Generalize the process for factoring trinomials of the form: X square-bx + c, x square –bx – c where b and c are positive integers and provide six example on the above tow form. ( 3 example on each form ).

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Example : x square + bx + c 1) x square + 17x + 42 =

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Example : x square + bx + c 2) n square + 2n + 35 =

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Example : x square + bx + c 3) 44 + 15h + h square =

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Example : x square - bx + c 1) -42- m + m square =

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Example : x square - bx + c 2) 40 – 22x + x square =

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Example : x square - bx + c 3) a square + 8a – 48 =

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Example : x square - bx - c 1) x square - 6x = 27

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Example : x square - bx - c 2) n square -120 = 7n

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Example : x square - bx - c 3) y square – 90 = 13y

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6.5 – Solving Equations with Quadratic Techniques.

6.5 – Solving Equations with Quadratic Techniques.

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