Question

Factor completely: x^2 − 3x − 10 @Compassionate

(x + 5)(x − 2)

(x − 10)(x + 1)

(x − 5)(x + 2)

(x + 10)(x − 1)

Answer 1

(x - 5)(x + 2) will be the correct answer

Answer 2

Hello, my name is Stephen and I'll be your tutor.

The first step is factoring the x-squared term. This isn't so hard.

(x )(x )

Now the second step is saying, "what are the multiples of -10 that add up to negative ."

5 * -2 = 10
But 5 - 2 =/= -3
So that's not it

Hmm... I wonder what it could be, hun?

Answer 3

That add up to negative what? > . <

Answer 4

That add up to negative 3, hun. What are two multiples of -10 that add up to negative 3.

Answer 5

Oh, It didn't show up, sorry. But two multiplies are 5 and -2.

Answer 6

Or you can think about it this way.

Which two numbers ADD t give you -3 and MULTIPLY to give you -10?

Answer 7

I can't think of any :/

Answer 8

"what are the multiples of -10"
You mean factors of -10, not multiples.

Answer 9

@unheard
Can you list all pairs of numbers that multiply to -10?
I'll do the first two for you:
-1, 10
-10, 1

Answer 10

-2, 5
5, -2

Answer 11

Great. Here are all 4 sets of pairs:
-1, 10
-10, 1
-2, 5
5, -2
Now can you write, at the end of each line, the sum of the two numbers.
I've done the first one for you (copy and paste the text below):
-1, 10; sum 9
-10, 1; sum
-2, 5; sum
5, -2; sum

Answer 12

-10, 1; sum -9
-2, 5; sum 3
5, -2; sum 3

Answer 13

Wait, notice your last two pairs are the same numbers.
You should have
-2, 5
-5, 2
Now do their sums.

Answer 14

Ohh, the last one is -3

Answer 15

Exactly. Since -5 and 2 multiply to -10 and add to -3, they are the factors of -10 you need.
Now the factoring is simply putting those two numbers inside the parentheses, as @compassionate shopwed you above:
x^2 − 3x − 10 =
(x )(x )
Now place -5 and 2:
(x - 5)(x + 2)

Answer 16

Thanks!

Answer 17

wlcm