Download Dave Calkins – Factoring Trinomials

Dave Calkins – Factoring Trinomials
Ex/ Factor: 12x2 – 7x – 12
(1) ab = 12 12 = 144 Now consider all the pairs of factors of 144.
(2) Note the ‘-’ before the ‘12’, which I call Type B (subtract…)
So we’re looking for a pair of factors which subtract to get ‘7’.
Ah ha! The 9&16 combination! And the ‘bigger number’ gets
the sign! Here the ‘-’ before the ‘7’. So we’ll use -16x and +9x.
(3) Now here comes the tricky part… Write out all four terms…
12x2 – 16x + 9x – 12 and group them in twos…
(12 x 2  16 x)   9 x  12  Now factor out the GCF for each pair…
4 x(3x  4)  3(3x  4) Notice the common factor of (3x – 4)…
(3x  4)(4 x  3) That’s it!
Ex/ Factor: 24x2 – 47x + 20
(1) ab = 24  20  480 Now consider all pairs of factors of 480.
(2) Note the ‘+’ before the ‘20’ which I call Type A (add…)
So we’re looking for a pair of factors that add to get ‘47’
Ah ha! The 15&32 combination! The signs are both negative.
So we’ll use -15x and -32x.
(3) Now that tricky part again… Write out all four terms…
24 x2  15x  32 x  20 Group them in pairs and factor…
3x(8x  5)  4(8x  5) Notice you’ll always find another GCF
(8 x  5)(3x  4) That’s it again!
Thanks David! Let’s try it on some easier (Type C) ones!
1,144
2,72
3,48
4,36
6,24
8,18
9,16
12,12
1,480
2,240
3,160
4,120
5,96
6,80
8,60
10,48
12,40
15,32
16,30
20,24
Ex/ Factor: 6x2 + 5x – 4
(1) ab = 24 so we’ll use 1&24 or 2&12, or 3&8 or 4&6
(2) Since this is a Type B (note the ‘-4’ on the end), we’ll subtract…
Ah ha! We’ll use the 3&8 pair. With 8 getting the ‘+’ from the middle ‘+5x’.
(3) 6x2 – 3x + 8x – 4 Now group in pairs and factor out the GCF’s…
3x(2x – 1) + 4(2x – 1) = (2x – 1)(3x + 4) Wow!
This if fun but perhaps for an Algebra 2 student. An Algebra 1 student should have trouble
with the ‘grouping’ in pairs thing and taking out GCF’s at two stages of the process.