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**Factoring Quadratic Equations**

Objective: To factor a quadratic expression and to use factoring to solve quadratic equations.

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Factoring We will be factoring many different types of quadratic equations. The first type we will look at is an expression containing two or more terms.

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Factoring We will be factoring many different types of quadratic equations. The first type we will look at is an expression containing two or more terms. The first thing that you will always do is to factor out the greatest common factor.

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Example 1

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Example 1

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Example 1

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Try This Factor each quadratic expression.

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Try This Factor each quadratic expression.

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Try This Factor each quadratic expression.

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Factoring ax2 + bx + c We will now look at factoring quadratic expressions where a is 1 and c is positive.

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Factoring ax2 + bx + c We will now look at factoring quadratic expressions where a is 1 and c is positive. We will start each problem by looking at factors of c.

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Factoring ax2 + bx + c We will now look at factoring quadratic expressions where a is 1 and c is positive. We will start each problem by looking at factors of c. We want these factors to add together to equal b.

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Factoring ax2 + bx + c We will now look at factoring quadratic expressions where a is 1 and c is positive. We will start each problem by looking at factors of c. We want these factors to add together to equal b. We want factors of c that add together to equal b.

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Factoring ax2 + bx + c We will now look at factoring quadratic expressions where a is 1 and c is positive. We will start each problem by looking at factors of c. We want these factors to add together to equal b. If b is positive, both terms will be ( x + ) and if b is negative, both terms will be (x - ).

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Factoring Factor the following.

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**Factoring Factor the following.**

We are looking for factors of 12 that add together to equal 7.

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**Factoring Factor the following.**

We are looking for factors of 12 that add together to equal 7. The factors of 12 are:

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**Factoring Factor the following.**

We are looking for factors of 12 that add together to equal 7. The factors of 12 are:

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You Try Factor the following.

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**You Try Factor the following.**

We are looking for factors of 18 that add together to equal 9. The factors of 18 are:

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**You Try Factor the following.**

We are looking for factors of 18 that add together to equal 9. The factors of 18 are:

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Example Factor the following.

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**Example Factor the following.**

We are looking for factors of 32 that add together to equal 12. The factors of 32 are:

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**Example Factor the following.**

We are looking for factors of 32 that add together to equal 12. The factors of 18 are:

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You Try Factor the following.

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**You Try Factor the following.**

We are looking for factors of 28 that add together to equal 11. The factors of 28 are:

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**You Try Factor the following.**

We are looking for factors of 28 that add together to equal 11. The factors of 28 are:

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**Factoring Now we will say factors of c that are different by b.**

We will now look at expressions where c is negative. Now we will say factors of c that are different by b. The larger factor has the same sign as b.

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Factoring Factor the following.

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**Factoring Factor the following.**

We are looking for factors of 30 that are different by 7. The factors of 30 are:

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**Factoring Factor the following.**

We are looking for factors of 30 that are different by 7. The factors of 30 are:

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You Try Factor the following.

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**You Try Factor the following.**

We are looking for factors of 27 that are different by 6. The factors of 27 are:

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**You Try Factor the following.**

We are looking for factors of 27 that are different by 6. The factors of 27 are:

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**Factoring We will now look at factoring when a is not 1.**

If c is positive, we are looking for the outer and inner to add together to equal b. If c is negative, we are looking for the outer and inner to be different by b. We need to start with factors of a. We will always choose the factors that are closet to each other.

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Factoring Factor the following.

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**Factoring Factor the following.**

We are looking for the outer and inner to add together to be 11. We will start with 2 and 3.

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**Factoring Factor the following.**

We are looking for the outer and inner to add together to be 11. We will start with 2 and 3. The outer is 3x and the inner is 6x. Do not add to equal 11.

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**Factoring Factor the following.**

We are looking for the outer and inner to add together to be 11. We will start with 2 and 3. The outer is 9x and the inner is 2x. Does add to equal 11.

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**Factoring Factor the following.**

We are looking for the outer and inner to add together to be 11. We will start with 2 and 3. The outer is 9x and the inner is 2x. Does add to equal 11.

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You Try Factor the following.

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**You Try Factor the following.**

We are looking for the outer and inner to be different by 11. We will start with 1 and 3.

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**You Try Factor the following.**

We are looking for the outer and inner to be different by 11. We will start with 1 and 3. The outer is 5x and the inner is 12x. Is not different by 11.

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**You Try Factor the following.**

We are looking for the outer and inner to be different by 11. We will start with 1 and 3. The outer is 4x and the inner is 15x. Is different by 11.

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**You Try Factor the following.**

We are looking for the outer and inner to be different by 11. We will start with 1 and 3. The outer is 4x and the inner is 15x. Is different by 11.

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**The Difference of Two Squares**

The word different means subtraction. When two perfect squares are being subtracted, there is a special way to factor this.

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**The Difference of Two Squares**

Factor the following.

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**The Difference of Two Squares**

Factor the following.

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You Try Factor the following.

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You Try Factor the following.

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You Try Factor the following.

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You Try Factor the following.

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**Factoring Perfect Squares**

If the first term and last term are both perfect squares, you should see if the trinomial factors as a perfect square.

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**Factoring Perfect Squares**

If the first term and last term are both perfect squares, you should see if the trinomial factors as a perfect square.

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**Factoring Perfect Squares**

Factor the following.

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**Factoring Perfect Squares**

Factor the following.

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Zero Product Property If two or more terms are being multiplied together and their product is zero, one of them must equal zero.

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Example 6

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Example 6

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Example 6

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You Try Use the zero product property to find the zeros of each function.

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You Try Use the zero product property to find the zeros of each function.

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You Try Use the zero product property to find the zeros of each function.

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You Try Use the zero product property to find the zeros of each function.

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You Try Use the zero product property to find the zeros of each function.

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Homework Page 296 31-65 odd This is a skill that is best learned by repetition. You need to do all of these problems and maybe more to become really good at this.

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Factoring x 2 + bx + c Section 9.5. Main Idea x 2 + bx + c = (x + p)(x + q) where p + q = b and pq = c.

Factoring x 2 + bx + c Section 9.5. Main Idea x 2 + bx + c = (x + p)(x + q) where p + q = b and pq = c.

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