9.8

Factoring by Grouping

9.8 – Factor by Grouping

Goals / “I can…”Factor polynomials with 4 termsFactor trinomials by grouping

9.8 – Factor by Grouping

Look at the following:

5t + 20t + 6t + 24

I can’t factor a fourth power.

4 3

9.8 – Factor by Grouping

BUT try grouping the terms together

(5t + 20t ) + (6t + 24)

Can I factor something in the first parentheses?

The second?

4 3

9.8 – Factor by Grouping

5t (t + 4) + 6(t + 4)

Notice, both have a (t + 4)

SO…

3

9.8 – Factor by Grouping

(5t + 6)(t + 4)3

Factor by GroupingExample 1:

FACTOR: 33xyxy - 21 - 21yy + 5 + 5xx – 35 – 35Factor the first two terms: 3xy - 21y = 3y (x – 7)Factor the last two terms: + 5x - 35 = 5 (x – 7)The blue parentheses are the same so it’s the

common factor Now you have a common factor

(x - 7) (3y + 5)

Factor by Grouping Example 2:

FACTOR: 66mxmx – 4 – 4m m + 3+ 3rxrx – 2 – 2rrFactor the first two terms: 6mx – 4m = 2m (3x - 2)Factor the last two terms: + 3rx – 2r = r (3x - 2) The blue parentheses are the same so it’s the

common factor Now you have a common factor

(3x - 2) (2m + r)

Factor by Grouping Example 3:

FACTOR: 1515xx – 3 – 3xyxy + 4 + 4yy –20 –20Factor the first two terms: 15x – 3xy = 3x (5 – y)Factor the last two terms: + 4y –20 = 4 (y – 5)The green parentheses are opposites so change

the sign on the 4 - 4 (-y + 5) or – 4 (5 - y)Now you have a common factor (5 – y) (3x – 4)

9.8 – Factor by Grouping

TRY:

6x + 3x – 4x – 23 2

9.8 – Factor by Grouping

TRY:

4n + 8n - 5n – 10 3 2

9.8 – Factor by Grouping

TRY:

12p + 10p - 36p – 30p4 3 2

9.8 – Factor by Grouping

9.8 – Factor by Grouping

9.8 – Factor by Grouping

You may have to rearrange the terms 1st

Now let’s try it with 3 termsCan we still group these?

6x + 5x + 12

9.6 – Factoring Trinomials

TRY:

6y + 23y + 72

9.6 – Factoring Trinomials

TRY:

7y - 26y - 82

9.6 – Factoring Trinomials

Look at the trinomial:

20y + 17y + 3 2

9.6 – Factoring Trinomials

TRY:

3y – 16y – 122

9.6 – Factoring Trinomials

TRY:

24y + 10y - 62