Factoring Quadratic Trinomials …beyond the guess and test method.

Topics 1. Standard FormStandard Form 2. When c is positive and b is positiveWhen c is positive and b is positive 3. When c is positive and b is negativeWhen c is positive and b is negative 4. When c is negativeWhen c is negative 5. When the trinomial is not factorableWhen the trinomial is not factorable 6. When a does not equal 1When a does not equal 1 7. When there is a GCFWhen there is a GCF

The standard form of any quadratic trinomial is Standard Form a=3 b=-4 c=1

Now you try. a = ?? b = ?? c = ?? Click here when you are ready to check your answers!

The standard form of any quadratic trinomial is Recall a = 2 b = -1 c = 5 Try Another!

a = ?? b = ?? c = ?? Go on to factoring!

Factoring when a=1 and c > 0. First list all the factors of c

Find the pair that adds to ‘b’ These numbers are used in the factored expression.

Now you try. Click here when you are ready to check your answers!

Recall So we get: Try some others! We need to list the factors of c.

(x+3)(x+3)(x+2)(x+3) (x+1)(x+6)(x+2)(x+3) Go on to factoring where b is negative!

Factoring when c >0 and b < 0. Since a negative number times a negative number produces a positive answer, we can use the same method. Just remember to use negatives in the expression!

Let’s look at We need a sum of -13 Make sure both values are negative! First list the factors of 12

Now you try. Click here when you are ready to check your answers!

Recall In this case, one factor should be positive and the other negative. We need a sum of -6 Try some others!

(x-3)(x-4)(x-3)(x+4) (x-2)(x-2)(x-1)(x-4) Go on to factoring where c is negative!

Factoring when c < 0. We still look for the factors of c. However, in this case, one factor should be positive and the other negative. Remember that the only way we can multiply two numbers and come up with a negative answer, is if one is number is positive and the other is negative!

Let’s look at In this case, one factor should be positive and the other negative. We need a sum of -1

Now you try. Click here when you are ready to check your answers!

Recall In this case, one factor should be positive and the other negative. We need a sum of 3 Try some others!

(x-3)(x+5)(x+3)(x-5) (x-5)(x+6)(x-6)(x-5) Go on to trinomials that are not factorable

Prime Trinomials Sometimes you will find a quadratic trinomial that is not factorable. You will know this when you cannot get b from the list of factors. When you encounter this write not factorable or prime.

Here is an example… Since none of the pairs adds to 3, this trinomial is prime.

Now you try. factorableprime factorableprime factorableprime Go on to factoring when a≠1

When a ≠ 1. Instead of finding the factors of c: Multiply a times c. Then find the factors of this product

We still determine the factors that add to b. So now we have But we’re not finished yet….

Since we multiplied in the beginning, we need to divide in the end. Divide each constant by a. Simplify, if possible. Clear the fraction in each binomial factor

Recall Divide each constant by a. Simplify, if possible. Clear the fractions in each factor Multiply a times c. List factors. Write 2 binomials with the factors that add to b Try some others!

Now you try. Click here when you are ready to check your answers!

(2x-1)(x+5)(2x+5)(x+1) (2x-5)(2x+1)(4x+5)(x-1) Go on to trinomials that have a GCF

Sometimes there is a GCF. If so, factor it out first

Now you try. Click here when you are ready to check your answers! 1. 2.

Recall First factor out the GCF Then factor the remaining trinomial. 9 times 2 = 18 Try some others!

6(x-1)(x+6)(6x+6)(x-6) 2(2x+1)(x+5)2(2x+5)(x+1) 1. 2.

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Good Job! You have completed Standard Form!

Good Job! You have completed factoring “When c is positive and b is positive”!

Good Job! You have completed factoring “When c is positive and b is negative”!

Good Job!

Good Job! You have completed factoring “When a does not equal 1”!

Good Job! You have completed factoring “When c is negative”!

Good Job!

Good Job! You have completed factoring “When there is a GCF”!

Review and Try Again!

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Review and Try Again!