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Chapter 8.2 Factoring Polynomials

Chapter 8.2 Factoring Polynomials. Objective One. Factor Trinomials in form of x 2 + bx + c. Determine if the Trinomial factors are the product of two binomials. When factoring Trinomials, there is a process of setting up the binomials that could prove useful.

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Chapter 8.2 Factoring Polynomials

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  1. Chapter 8.2 Factoring Polynomials Objective One

  2. Factor Trinomials in form of x2 + bx + c • Determine if the Trinomial factors are the product of two binomials. • When factoring Trinomials, there is a process of setting up the binomials that could prove useful. • The signs of the binomials are determined by the sign of the last and coefficient of the x term.

  3. Determining the Signs of the binomials. • If the sign of the last term is negative, then the signs of the binomials are opposites. • If the sign of the last term is positive, then the signs of the binomials are the same, and determined by the sign of the coefficient of the x term.

  4. Determining the Signs of the binomials • x2 + bx – c = ( - )( + ) • x2 + bx + c = ( + )( + ) • x2 - bx + c = ( - )( - )

  5. Determining the variables and constants of the binomial • The first terms of the binomials are derived from the First times First of FOIL. • x2 + bx – c = (x - )( x + ) • The last terms of the binomials are derived from the factors of the Last term of the trinomial. • AND • The factors are to the OO and II from the FOIL and must sum to the coefficient of the x term of the trinomial.

  6. Using the information, Factor x2-8x+15 • 1st set up binomials with the signs. • ( - )( - ) • 2nd insert factors of x2 (x - )(x - ) • Factors of 15 Sum • 1,15 16 • 3,5 8 ( x - 3)( x - 5) • Check by FOIL!

  7. Factor x2-6x-16 • 1st set up binomials with the signs. • ( + )( - ) • 2nd insert factors of x2 (x + )(x - ) • Factors of -16 Sum • 1,-16 -15 • -1,16 15 • -2, 8 6 • 2,-8 -6 • -4,4 0 • ( x + 2)( x - 8) • Check by FOIL!

  8. Factor x2+3x-18 • 1st set up binomials with the signs. • ( + )( - ) • 2nd insert factors of x2 (x + )(x - ) • Factors of -18 Sum • 1,-18 -17 • -1,18 17 • -2, 9 7 • 2,-9 -7 • -3,6 3 • 3,-6 -3 • ( x + 6)( x - 3) • Check by FOIL!

  9. 8.2 Objective 2 • Factor Completely • Sometimes, a common factor must be extracted in order to factor a trinomial, or to simplify factoring.

  10. Factor 3x3+15x2+18x • Factor GCF3x(x2+5x+6) • 1st set up binomials with the signs. • 3x ( + )( + ) • 2nd insert factors of x2 3x( x + )(x + ) • Factors of 6 Sum • 1,6 7 • 2,3 5 3x( x + 3)( x + 2) • Check by FOIL!

  11. Factor 3x2y-18xy-81y • Factor GCF 3y(x2-6x-27) • 1st set up binomials with the signs. • 3y ( + )( - ) • 2nd insert factors of x2 3y(x + )(x - ) • Factors of -27 Sum • 1,-27 -26 • -1,27 26 • -3, 9 6 • 3,-9 -6 • 3y ( x + 3)( x - 9) • Check by FOIL!

  12. Factor 4x2-40xy+84y2 • Factor GCF 4(x2-10xy+21y2) • 1st set up binomials with the signs. • 4 ( - ) ( - ) • 2nd insert factors of x2 & y2 4(x - y) (x - y) • Factors of 21 Sum • -1,-21 -22 • -3,-7 -10 • 4 ( x - 3y)( x - 7y) • Check by FOIL!

  13. NOW YOU TRY! • 1. x2- 8x+12 • 2. x2+8x+12 • 3. x2+ 7x+12 • 4. x2- 4x -12 • 5. 3x2+6x-72 • 6. 2x2+ 6x-20

  14. ANSWERS • 1. (x-6)(x-2) • 2. (x+6)(x+2) • 3. (x+4)(x+3) • 4. (x-6)(x+2) • 5. 3(x+6)(x-4) • 6. 2(x+5)(x-2)

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