Question

Factor completely: 2x2 + 6x − 80

(2x − 5)(x + 8)

(2x − 10)(x + 8)

2(x − 5)(x + 8)

2(x − 10)(x + 8)

Answer 1

\[2x^2+6x-80=2(x^2+3x-40)=2(x+?)(x-?)\]

Answer 2

the first question is 8 and the second question is 5
since 8(-5)=-40
and 8+(-5)=3

Answer 3

\[\large 2x^2 + 6x - 80\]



\[\large 2(x^2 + 3x - 40)\]



\[\large 2(x^2 + 8x-5x - 40)\]



\[\large 2(x(x + 8)-5(x +8))\]



\[\large 2(x-5)(x + 8)\]
So the answer is choice C

Answer 4

one day i am going to learn this factor by grouping thing

Answer 5

satellite i thought i taught you :(

Answer 6

yes you did. you taught me, but i didn't learn it. (you been there before i am sure). care to try again?

Answer 7

\[ax^2+bx+c\]
to factor something of this form:
Find factors of a*c that have product a*c and have sum b

Answer 8

we got
\[x^2+3x-40\] and please don't say "two numbers whose product is -40 and whose sum is 3" because that is how i do it

Answer 9

lol

Answer 10

that is the same thing as "factoring" without grouping.

Answer 11

factor by grouping is how i did that one proof on the quadratic formula

Answer 12

factor by grouping is the coolest!

Answer 13

oooh right. like completing the square. or that great sophie germain trick

Answer 14

i remember that trick a bit

Answer 15

oh jim hasn't seen my proof on the quad formula yet : 0

Answer 16

Example: Factor 9x^2-6x-8

Step 1) Multiply the first and last coefficients: 9*(-8)=-72

Step 2) Find two numbers that both multiply to -72 and add to -6. Those numbers are -12 and 6

Step 3) Replace -6x with -12x+6x (notice how -12x+6x adds back to -6x). The -12x and -6x are drawn exactly from those two numbers we found in step 2). So 9x^2-6x-8 turns into 9x^2-12x+6x-8

Step 4) Now factor the expression by grouping


9x^2-12x+6x-8


(9x^2-12x)+(6x-8) ... pair off terms in 2 groups (how you pair depends on the problem)


3x(3x-4)+(6x-8) ... factor out the GCF 3x from the first group


3x(3x-4)+2(3x-4) ... factor out the GCF 2 from the second group


Notice we now have a common factor of 3x-4, factor this out to get (3x+2)(3x-4)


So 9x^2-6x-8 = (3x+2)(3x-4)

Answer 17

i like jim's explanations

Answer 18

so perfect

Answer 19

the pdf isn't showing up for me...

Answer 20

like when you click it, it doesn't show anything?

Answer 21

apparently it doesn't like firefox, but chrome works fine, weird...

Answer 22

well completing the square is still a better way to prove the quadratic formula but this works too

Answer 23

i am a big fan of completing the square in all circumstances except finding a vertex (lol)

Answer 24

for example in factoring
\[x^4+x^2+1\]