Question

The quadratic expressions \(x^2+5x−14\) and \(49-x^2\)​​ share a common binomial factor.

Answer 1

So, what's the question? Are we supposed to factor it out?

Answer 2

They do.

Answer 3

Yes. @YanaSidlinskiy I need help doing that.

Answer 4

first take x out of the quadratic function

Answer 5

But one is negative and one isn't..

Answer 6

oh sorry
you can simplify first
(x^2+5x−14x^2
= 5x - 13x^2
= x(5 - 13x)

Answer 7

there are no common factors here
are you sure you have the question right?

Answer 8

The 14 isn't supposed to have \(x^2\)

Answer 9

i suspect thet the quadratic is x^2+5x−14

Answer 10

right

Answer 11

Sorry about that.

Answer 12

to factor x^2+5x−14 you need to find 2 numbers whose product is -14 and whose sum is
+5

Answer 13

can you tell me what those 2 numbers sre?

Answer 14

think of the factors of -14

Answer 15

Their product has to be -14 but the sum has to be 5?

Answer 16

yes

Answer 17

Hm.. I don't really know, but I know for the -14..

Answer 18

-14 = -7 * 2 or
-14 = -2 * 7

Answer 19

which 2 factors add up to +5?

Answer 20

-2+7

Answer 21

right on
so the factors of (x^2+5x−14)
are ( x - 7)(x + 2)

Answer 22

if you expand this function you'll see it works out to x^2 + 5x - 14

Answer 23

* oops my bad
its (x + 7)(x - 2)

Answer 24

Yes. Thank you so much.

Answer 25

Now you need to factor x^2 - 49

Answer 26

Okay.

Answer 27

can u do that?

Answer 28

49 - x^2

Answer 29

(x-7)(x+7) ? I don't know..

Answer 30

49 - x^2 = (7 - x)(7 + x)

so can you see the common factor?

Answer 31

Yes.

Answer 32

x + 7

Answer 33

Oh, okay. Thanks a bunch.