Question

Factor completely: x^3 − 2x^2 − 5x + 10.

(x − 2)(x^2 − 5)
(x + 2)(x^2 + 5)
(x − 2)(x^2 + 5)
(x + 2)(x^2 − 5)

Answer 1

oofff
do you know how to divide polynomials by stuff
ex. ^^^^^^^^^^^^^^^^^^^^^^^^^ divided by (x-2) or (x+2)

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
oofff
do you know how to divide polynomials by stuff
ex. ^^^^^^^^^^^^^^^^^^^^^^^^^ divided by (x-2) or (x+2)
\(\color{#0cbb34}{\text{End of Quote}}\)
not really

Answer 3

@AZ

Answer 4

This one can be solved by factoring by grouping

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
This one can be solved by factoring by grouping
\(\color{#0cbb34}{\text{End of Quote}}\)
ok, so what do I do

Answer 6

So this is an example of factoring by grouping:

Answer 7

So we have

x^3 - 2x^2 - 5x + 10

we'll split it into two and factor it
and if we get the same factor for both halves, we can then factor that common factor

Answer 8

ok

Answer 9

what can you factor out of

x^3 - 2x^2

Answer 10

x^2(x-2)

Answer 11

Good!

now what about

-5x+10

Answer 12

-5(x-2)

Answer 13

Good!

so now we went from
x^3 - 2x^2 - 5x + 10

to
x^2(x-2) -5(x-2)

so we can factor out the (x-2)

Answer 14

when you look at it, you should see it now as 2 terms

x^2(x-2) - 5(x-2)

so from this, we're factoring out (x-2) because it's common in both terms

Answer 15

ok, so its A or C

Answer 16

so let's get rid of all those crazy numbers and exponents and look at a simpler example

you have

ab - ac

if you factor out a, we'll get
a(b-c)

so think of (x-2) as our a
what are you left with?

Answer 17

idk

Answer 18

so if we have

ax^2 - 5a

what do you get if you factor out the a?

Answer 19

oh, a(x^2 - 5)

Answer 20

there you go!

and instead of a, we can just replace it with our (x-2)

since that was the common factor

Answer 21

ok, so its A?

Answer 22

that's your answer!

Answer 23

Thanks!!

Answer 24

You're welcome!