Question

Factor each trinomial below. Please show your work.
1.x2 – 8x + 15
2.a2 – a – 20
3.a2 – 5a – 20
4.a2 + 12ab + 27b2
5.2a2 + 30a + 100

Answer 1

I'll do the first one to get you started

Answer 2

ok thanks!

Answer 3

you need to find two numbers that multiply to 15 (last term) and add to -8 (middle coefficient)

these two numbers are -3 and -5 since -3*(-5) = 15 and -3 + (-5) = -8

so this means

x^2 - 8x + 15 factors to (x-3)(x-5)

Answer 4

this trick only works if the leading coefficient is 1

Answer 5

ok so it will work for the first 4?

Answer 6

correct, #4 is a bit different but it's basically the same as the first 3

Answer 7

ok now what about the last one?

Answer 8

for #4, instead of saying

(a+NUMBER1)(a+NUMBER2)

you would say

(a+NUMBER1*b)(a+NUMBER2*b)

where NUMBER1 and NUMBER2 are the two numbers you found

Answer 9

then what would 'b' be?

Answer 10

the third number?

Answer 11

because 2 goes into each coefficient, you can factor out 2 to get

2a^2 + 30a + 100

2(a^2 + 15a + 50)

now factor a^2 + 15a + 50 and keep the 2 outside in mind

Answer 12

no b is just a variable

Answer 13

ok

Answer 14

look at #4 and notice you have the two variables a and b

Answer 15

ya but there is no sqr. rt of 50 but you could /2 again...?

Answer 16

*#5

Answer 17

ok...

Answer 18

2a^2 + 30a + 100

2(a^2 + 15a + 50)

2(a+10)(a+5) ... since 10+5 = 15 and 10*5 = 50

Answer 19

see how I'm getting that?

Answer 20

oh ok so that would be the answer right?

Answer 21

yeah

Answer 22

ok

Now that makes sense! Thanks!

Answer 23

yw