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Factoring Trinomials

Factoring Trinomials. Section 5.5. Objective. To factor a remaining expression with three terms (trinomial). Factor. Factor 20(find a multiplication problem). We start with any 2 factors. 20. The question is….

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Factoring Trinomials

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  1. Factoring Trinomials Section 5.5

  2. Objective • To factor a remaining expression with three terms (trinomial).

  3. Factor • Factor 20(find a multiplication problem). We start with any 2 factors. 20 The question is…. Can we continue factoring the remaining expression just like we can continue factoring the 4. This first step is equivalent to our first step of factoring the GCF. 5 4 Cannot factor the 5 any further We can continue factoring the 4  we can find a multiplication problem for 4. 2 2 5

  4. Factoring • The first step to factoring ANY expression…Factor the GCF. • The next step to factoring is to see if you can write a multiplication problem for the remaining expression. Example: Factor 2x3 – 4x2 + 6x First Step: 2x(x2 – 2x + 3) Next Step: Can we write a multiplication problem for this expression?

  5. Writing a multiplication problem for the remaining expression. • The method we use to write a multiplication problem for the remaining expression depends on how many terms the expression contains.

  6. Factoring Step 1: Factor the GCF  GCF (Remaining Expression) Step 2: Factor the remaining expression, if possible. If the Remaining Expression has… Threeterms Four or moreterms Use “backwards” FOIL Use Factor by Grouping to factor the remaining expression. Must be in the form: Axn + Bxn/2 + C ; A, B, C are numbers.

  7. Factoring Trinomials • If the remaining expression contains 3 terms, we call it a trinomial. • Trinomials that are in the “right” form. • 2x4 – 5x2 – 2 • 3x6 + 3x3 + 1 • 5x2 + 6xy – y2 • Trinomials that are not in the “right” form. • 5x3 + 4x + 1 • 5z2 + 3 – 4x

  8. Factoring Trinomials When you multiply the first terms = first term of the trinomial Factor: 2x2 + 7x + 6 First Outer Inner Last The trinomial is in the right form. Step 1: No GCF Step 2: Factor the trinomial ( 2x ) ( x ) 1 2 3 6 6 1 3 2 Outers + Inners = Middle term. Use “backward” FOIL Which is correct? When you multiply the last terms = last term of the expression.

  9. Factor Trinomials Factor: 2x2 + 7x + 6 Try one combination, if it doesn’t work, try another. (2x 3)(x 2 ) Let’s try: + + Inners + 3x 4x + Outers 7x Middle Term

  10. Examples • Factor: 6x4 + 19x2 + 10 The trinomial is in the right form. 1. NO GCF ( )( ) 2x2 5 2 3x2 You have several choices, 2 and 5, 5 and 2, 1 and 10, and 10 and 1. This product must equal 10. Try 5 and 2 This product must equal 6x4. Try 2x2 , 3x2

  11. Examples Let’s check if we have the right combination. • Factor: 6x4 + 19x2 + 10 (2x2 5)(3x2 2) + + inners 15x2 + Both need to be positive to get 19x2 4x2 outers + 19x2 Middle term

  12. Examples • Factor: -5p3 + 50p2 – 125p 1. GCF = -5p -5p(p2 – 10p + 25) Trinomial is in the right form. -5p( )( ) p p 5 - - 5 Inners 5p Both have to be negative to get -10p. Product has to equal p2. Try 5 and 5. Can be 1 and 25 or 5 and 5. 5p Product has to equal 25. Outers

  13. Try These • Factor: 2a2 + 15ab – 27b2 Click to check your answer. (2a - 3b)(a + 9b )

  14. Try These • Factor: 2x2 + 2x - 10 Click to check your answer. 2(x2 + x – 5)

  15. Try These • Factor: 12x2 – 5x – 2 Click to check your answer. (3x - 2 ) ( 4x + 1)

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