Factor by Grouping

Factor by Grouping

Poll

Which winter sport is the best?

• Skiing

• Snowboarding

• Skating

• Sledding

Factor by Grouping

A polynomial can be factored by grouping only if these conditions exist:

• There are 4 or more terms

• Terms have common factors that can be grouped together

• There are two common factors that are identical or additive inverses of each other​

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ax + bx + ay + by = (ax + bx) + (ay + by)

= x(a + b) + y(a + b)

= (x + y)(a + b)​

Some text here about the topic of discussion

Step 1: Group terms with common factors

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Step 2: Factor the GCF from each group

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Step 3: Distributive Property​​

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4qr + 8r + 3q +6

Multiple Choice

rn + 5n - r - 5

• (r - 1)(5 + n)

• (r + 5)(n - 1)

• r(n + 5n - 6)

• 5r(n - 1)

Multiple Choice

3np + 15p - 4n - 20

• (3p + 5)(n - 4)

• 3p - 4(n + 5)

• (3p - 4)(n + 5)

• 3p - 4 + n + 5

​Additive Inverse

two values, when ​added together, that cancel out

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the additive inverse of 2ab is -2ab​

Step 1: Group terms with common factors

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Step 2: Factor the GCF from each group

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Step 3: Additive Inverse

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Step 4: Distributive Property​

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2mk - 12m + 42 - 7k

Multiple Choice

Which of these is an example of additive inverse?

• -6a + 6ab

• 12xy - 6xy

• 20x - 15x - 5x

• -6x + 2x - 4x

Multiple Choice

c - 2cd + 8d - 4

• c - 4(1 - 2d)

• (c - 1)(2d - 4)

• (c + 4) - (2d - 1)

• (c - 4)(1 - 2d)

3(0) =

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0(2 - 2) =

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-312(0) =

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0(0.25) =​

If a product of two factors is 0, at least one of the factors MUST be 0

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For any real numbers a and b, if ab = 0, then a = 0, b = 0, or both​

​Zero Product Property:

Solve Equations by Factoring

Step 1: Get 0 on one side of the equation​

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Step 2: Zero Product Property

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Step 3: Solve each equation using inverse operations (remember first semester!)​

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Answer: Write your answer in terms of solutions or roots.​​

(2d + 6)(3d - 15) = 0

Step 1: Get 0 on one side of the equation​

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Step 2: Zero Product Property

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Step 3: Solve each equation using inverse operations (remember first semester!)​

c² = 3c

Fill in the Blanks

Solve by factoring:

x² = -10x

Poll

How confident do you feel about this lesson?

• Very Confident

• Confident

• Unsure

• Not Confident