Warm up Factor completely Factoring by Grouping SWBAT
Warm up Factor completely
Factoring by Grouping SWBAT: Given 4 terms completely factor the given polynomial SWBAT: Factor a trinomial using grouping
To Factor using grouping you must have EXACTLY 4 terms.
Ex. 1: 5 x + 15 + xy + 3 y Step 1: Factor GCF Done Step 2: Break the terms into 2 parts – group 1 st 2 together and last 2 together Step 3: factor each part separately (5 x + 15) (xy + 3 y) 5(x + 3) + y(x + 3) Hint: What’s inside the parenthesis should match. Step 4: Write your answer Step 5: Check your answer – multiply it out. (x + 3)(5 + y) 5 x + 15 + xy + 3 y
Ex 2: 2 xy - 4 ya + 10 x – 20 a Step 1: GCF Step 2: 2 groups Step 3: Factor each group Step 4: Write answer Step 5: Check answer 2(xy – 2 ya + 5 x – 10 a) 2(xy – 2 ya) (+5 x – 10 a) 2[y(x – 2 a) +5(x – 2 a)] 2(x – 2 a) (y + 5) 2 xy – 4 ya + 20 a – 10 x
Ex 3: 18 x 3 + 6 x 2 +3 x+1 l St 1 – done l St 2 (18 x 3 + 6 x 2) (3 x + 1) l st 3 6 x 2 (3 x + 1) 1 (3 x+1) 6 x 2/6 x 2 = 1 l St 4 (6 x 2 + 1)(3 x+1) If they have no common factor you must put 1
Ex 4: 4 x 2 – 8 xy – 3 x + 6 y Step 2: (4 x 2 – 8 xy) ( – 3 x + 6 y) 3 rd Step 3: 4 x (x – 2 y) -3(x – 2 y) Step 4: (x – 2 y) (4 x – 3) Step 5: 4 x 2 – 8 xy – 3 x + 6 y Hint: if the term is negative you must factor out a negative.
You try this one. Ex 5: 5 x 2 – 20 x 2 y + 5 a – 20 ay Remember to factor out anything that all terms have in common! 5(x 2 – 4 x 2 y + a – 4 ay) Answer: 5(x 2 + a) (1 – 4 y)
Homework: Factoring ws #6 Factoring by Grouping
- Slides: 9