A5-3 A/B Factoring with Negatives and a=/1

Lesson Objective:
Students will be ale to factor quadratics that contain negative numbers.
Students will be able to factor quadratic equations when the "a" value is not equal to 1 (A/B level)

Multiply out (either with an area model or distribution) the four pairs of binomials below. You should do them on your own paper; you'll want to be able to look back at them to answer the questions below.

Remember that quadratics often have the form:

In these examples, the "a" value is 1. 

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When both numbers (the 9 and 5 in the example above) are positive, what is true about the "b" and "c" values?

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When the "bigger" number (9 in this case) is negative and the smaller number (5) is positive, what is true about the "b" and "c" values?

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When the "bigger" number (9 in this case) is positive and the smaller number (5) is negative, what is true about the "b" and "c" values?

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When both numbers are negative, what is true about the "b" and "c" values?

Finding factors that add to a specific number is part of this process. Some people can do this pretty easily, but others need a more clear process, especially when negative numbers are involved. Try the problems below.

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What two numbers multiply to equal 20 and add to equal 12?

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What two numbers multiply to equal -30 and add to equal -1

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What two numbers multiply to equal 30 and add to equal -13

If that part was difficult, the video below describes an organizational tool and process to help figure out those numbers.

Use the skill you just learned and the patterns you recognized from A5-2 to factor the quadratics below.

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Factor the equation below.

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Factor the equation below.

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Factor the equation below.

If you struggled with those, watch the video below. The C-level of A5-3 has more practice with a=1 quadratics.

The next part will start to get into the A/B level skill for this unit. We need to make sure you know what "greatest common factor" means. The greatest common factor (referred to as GCF after this) is the largest number that two numbers can be divided by to get a whole number. For example, the GCF of 8 and 10 is 2. 
Sometimes, the greatest common factor is one of the numbers. For example, the GCF of 3 and 9 is 3. And sometimes, the only number both numbers can be divided by is 1.

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What is the greatest common factor of 12 and 20?

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What is the greatest common factor of 7 and 21?

Now we're going to factor out a GCF. To see how to do that, watch the video below.

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Find the factored form of the expression below by factoring out the GCF.

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Find the factored form of the expression below by factoring out the GCF.

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Find the factored form of the expression below by factoring out the GCF.

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Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.

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Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.

Now, we need to put all this together so we can factor quadratics where "a" isn't equal to zero. There are several methods people use for this, but the video below will show you a helpful tool for factoring these types of quadratics.

The practice for these will require that you show work. You can either do the work on the "Show your work" board, or take a picture of your paper and put it on the board.

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Factor the following quadratic.

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Factor the following quadratic.

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Factor the following quadratic.

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A5-3 A/B Factoring with Negatives and a=/1

When both numbers (the 9 and 5 in the example above) are positive, what is true about the "b" and "c" values?

When the "bigger" number (9 in this case) is negative and the smaller number (5) is positive, what is true about the "b" and "c" values?

When the "bigger" number (9 in this case) is positive and the smaller number (5) is negative, what is true about the "b" and "c" values?

When both numbers are negative, what is true about the "b" and "c" values?

What two numbers multiply to equal 20 and add to equal 12?

What two numbers multiply to equal -30 and add to equal -1

What two numbers multiply to equal 30 and add to equal -13

Factor the equation below.

Factor the equation below.

Factor the equation below.

What is the greatest common factor of 12 and 20?

What is the greatest common factor of 7 and 21?

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.Type your answer in without spaces.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.Type your answer in without spaces.

Factor the following quadratic.

Factor the following quadratic.

Factor the following quadratic.

Factor the following quadratic.

When both numbers (the 9 and 5 in the example above) are positive, what is true about the "b" and "c" values?

When the "bigger" number (9 in this case) is negative and the smaller number (5) is positive, what is true about the "b" and "c" values?

When the "bigger" number (9 in this case) is positive and the smaller number (5) is negative, what is true about the "b" and "c" values?

When both numbers are negative, what is true about the "b" and "c" values?

What two numbers multiply to equal 20 and add to equal 12?

What two numbers multiply to equal -30 and add to equal -1

What two numbers multiply to equal 30 and add to equal -13

Factor the equation below.

Factor the equation below.

Factor the equation below.

What is the greatest common factor of 12 and 20?

What is the greatest common factor of 7 and 21?

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the expression below by factoring out the GCF.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.Type your answer in without spaces.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.Type your answer in without spaces.

Factor the following quadratic.

Factor the following quadratic.

Factor the following quadratic.

Factor the following quadratic.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.

Find the factored form of the quadratic represented in the area model below. You can do your work on paper or on the "Show Your Work" board.

Type your answer in without spaces.