9.3 & 9.4 factoring trinomials by grouping p

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9.3 & 9.4 Factoring Trinomials by Grouping p.

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9.3 & 9.4 Factoring Trinomials by Grouping p. Review: (y + 2)(y + 4). First terms: Outer terms: Inner terms: Last terms: Combine like terms. In this lesson, we will begin with y 2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer. Factor y 2 + 6y + 8. - PowerPoint PPT Presentation

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Page 1: 9.3 & 9.4 Factoring Trinomials  by Grouping p

9.3 & 9.4Factoring Trinomials

by Grouping

p.

Page 2: 9.3 & 9.4 Factoring Trinomials  by Grouping p

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

y +2

y

+4

Review: (y + 2)(y + 4)

In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.

Page 3: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor y2 + 6y + 8Do we have a GCF?

Is it a Diff. of Squares problem?

Now we will learn Trinomials! You will set up a table with the following information.

Product of the first and last coefficients

Middlecoefficient

The goal is to find two factors in the first column that add up to the middle term in the second column.

Page 4: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor y2 + 6y + 8Create your table.

Multiply Add+8 +6

Product of the first and last coefficients

Middlecoefficient

Here’s your task…What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write

the combinations.

M

A

Page 5: 9.3 & 9.4 Factoring Trinomials  by Grouping p

We have two groups!

Find the GCF of each group and factor it out.

You can check it by multiplying (FOIL).

Page 6: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor x2 – 2x – 63 Do we have a GCF? NO! …

so, Create your table.Multiply AddProduct of the

first and last coefficients

Middlecoefficient

Signs need to be different

since number is negative.

M

A

Page 7: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Replace the middle term with working numbers.

Group the terms.

Factor out the GCF

The parentheses are the same!

Page 8: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Here are some hints to help you choose your factors in the table.

1) When the last term is positive, the factors will have the same sign as the middle term.

2) When the last term is negative, the factors will have different signs.

Page 9: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor 5x2 - 17x + 14 Do we have a GCF? NO! …

so, create your table.Multiply Add

Replace the middle term.

Group the terms.

M

A

Page 10: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor out the GCF

The parentheses are the same!

Hopefully, these will continue to get

easier the more you do them.

Page 11: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor 2x2 - 14x + 12

Multiply Add

Find the GCF!

Signs need to be the same as

the middle sign since the

product is positive.

Replace the middle term.

Group the terms.

Page 12: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor out the GCF

The parentheses are the same!

Remember: Always look for a GCF first!!

Page 13: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor x2 + 3x + 21. (x + 2)(x + 1)

2. (x – 2)(x + 1)

3. (x + 2)(x – 1)

4. (x – 2)(x – 1)

Page 14: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor 2x2 + 9x + 101. (2x + 10)(x + 1)

2. (2x + 5)(x + 2)

3. (2x + 2)(x + 5)

4. (2x + 1)(x + 10)

Page 15: 9.3 & 9.4 Factoring Trinomials  by Grouping p

Factor 6y2 – 13y – 51. (6y2 – 15y)(+2y – 5)

2. (2y – 1)(3y – 5)

3. (2y + 1)(3y – 5)

4. (2y – 5)(3y + 1)