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Factoring Trinomials of the form ax 2 +bx+c with a 0. Dr. Marcia L. Tharp

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Why learn to factor trinomials? Factoring trinomials is an important Algebraic skill. It is used in higher- level mathematics and science. Besides that you will need it to simplify polynomial expressions and solve more complex equations.

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Lesson 1 - Recognizing The Form ax 2 +bx+c with a 0 The trinomials we will factor that have the form ax 2 +bx+c where a 0 and a, b, and c are real numbers. For example in ax 2 +bx+c Let a=1, b=2 and c=4 Then we get a trinomial 1x 2 +2x+4 Remember 1 x 2 means x 2. So we can write x 2 +2x+4 too which fits this form.

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More Examples Lets look at some more examples where we will replace the values a, b, and c in the form ax 2 +bx+c. This time we get a trinomial 3x 2 +20x+12 which fits the form we are going to try to factor. since a 0 and a, b, and c are real numbers. If a=3, b=20 and c=12 do we get a trinomial that will fit our form that we will factor?

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What happens if we let a=4, b=0 and c=25? Will we get the trinomial form we need when we will replace the values a, b, and c in the form ax 2 +bx+c? Instead we get the binomial 4x 2 +25 which we will not factor here. It only has 2 terms so it is not a trinomial we are going to factor. This fits the form since a 0 where a, b, and c are real numbers. However, we wont discuss this here since we have already covered factoring binomials.

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What happens if we let a=0, b=3 and c =4 when we replace the values a, b, and c in the form ax 2 +bx+c ? This is not a trinomial of the form we need because a=0. The x 2 term is missing so it does not fit the form. It is a binomial. So we will not discuss factoring it using the methods in this section. Another Example We get 0x 2 +3x+4 = 3x+4.

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Lets try letting a=0, b=0, and c=5 when replace the values a, b, and c in the form ax 2 +bx+c. This is not a trinomial because a=0 and b=0. It is a monomial. Furthermore the x 2 term is missing since a equals 0 and it does not fit the form we are looking for above. We get 0x 2 +0x+5 = 5

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Time To Check Your Understanding. Check your understanding. Click on the expressions below that fit the form we want to factor. Remember we want to use polynomials of the form ax 2 +bx+c where a 0 and a, b, and c are real numbers that are not binomials. a. x 2 +6x+8x 2 +6x+8 b. x 2 +16x 2 +16 c. 2x+82x+8 d. 2x 2 +7x+62x 2 +7x+6

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Now click on the door to go on to How to factor the form ax 2 +bx+c with a =1

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Excellent you recognized the trinomial did have the form we are going to factor: ax 2 +bx+c where a 0 and a, b, and c are real numbers. Excellent you recognized the trinomial did have the form we are going to factor: ax 2 +bx+c where a 0 and a, b, and c are real numbers. Click the here to return to the presentation.here

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This is an incorrect response to Check Your Understanding.This is a binomial. We cover factoring binomials in another lesson. Click here to return to the presentation.here

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This is an incorrect response to Check Your Understanding.This is a binomial and a =0 so it does not have the term ax 2. Click the here to return to the presentation.here

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