Question

Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible.

The function f(x) is a difference of squares.
The function g(x) is a sum of squares.
The function h(x) is a perfect square trinomial.
The function j(x) can only have a GCF factored out of it.

Answer 1

@ganeshie8

Answer 2

for f(x).

you may use below identity
\(a^2-b^2 = (a+b)(a-b)\)

Answer 3

you can define f(x) like below :-

\(f(x) = x^2-2^2\)

Answer 4

and factor it using above identity

Answer 5

so we take f(x) = x^2 - 2^2 and factor it?

Answer 6

yup !

Answer 7

Can you walk me through factoring it?

Answer 8

did u look at the identity ?

Answer 9

my first reply...

Answer 10

alright so we factor it using a^2 - b^2 = (a + b)(a - b)
f(x) = x^2 - 2^2

so...
x^2 - 2^2 = (x + (-2)(x - (-2)?

Answer 11

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

thats it

Answer 12

So thats the answer for part 1?

Answer 13

you there @ganeshie8

Answer 14

yes

Answer 15

for g(x),
just create a quadratic wid SUM of two squares :-

\(g(x) = x^2+2^2\)

Answer 16

you cannot factor this, so nothing much to do.
move to h(x)

Answer 17

i want you try h(x), can u ? :)

Answer 18

one sec this takes time lol

Answer 19

(x − 5) * (x − 5)?

Answer 20

Yes !

Answer 21

:D

Answer 22

multiply and show it as trinomial like :-

\(ax^2+bx+c\)

Answer 23

\(h(x) = (x-5)^2 = ?\)

Answer 24

I'm not sure

Answer 25

\(h(x) = (x-5)^2 = (x-5)(x-5) = ?\)

Answer 26

you knw how to multiply right ?

Answer 27

yeah

Answer 28

-5x^2? lol

Answer 29

yo wat happened to u.. u use to be so good few days back on these :o

Answer 30

\((x-5)(x-5)\)

FOIL

\((x^2-5x - 5x +25\)

\(x^2-10x +25\)

\(h(x) = x^2-10x+25\)

Answer 31

Fine ?

Answer 32

lol been busy

Answer 33

I can see, you need to revise quick and get back on track ok

Answer 34

you should knw how to multiply

(x-5)(x-5)

Answer 35

alright I think I'm good, I forgot about foil lol

Answer 36

ive see u doing these before.. .just now you're acting like u lost all ur memory

Answer 37

*seen

Answer 38

for j(x), try something like below :-
\(j(x) = 2x^2 + 4\)

Answer 39

you can oly factor out the GCF there,
wats the GCF above ?

Answer 40

2

Answer 41

good :)
factor it out

Answer 42

\(j(x) = 2x^2 + 4 = 2(x^2+2)\)

Answer 43

thats it !
we have 4 functions, and factored them also

Answer 44

Thanks man!
Sorry I'm a bit rusty, been a while since I've delt with factoring xD

Answer 45

The function f(x) is a difference of squares.
\(f(x) = x^2-4\)
factored form : \(f(x) = (x+2)(x-2)\)


The function g(x) is a sum of squares.
\(f(x) = x^2+4\)
factored form : \(CANNOT ~ FACTOR\)


The function h(x) is a perfect square trinomial.
\(f(x) = x^2-10x+25\)
factored form : \(f(x) = (x-5)(x-5)\)


The function j(x) can only have a GCF factored out of it.
\(f(x) = 2x^2+4\)
factored form : \(f(x) = 2(x^2+2)\)

Answer 46

Enjoy...

Answer 47

hey np, it wont take much time for u to revise things...