Question

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Factor f(x) = x^3 + x^2 – 4x – 4 = 0 completely showing all work.

Answer 1

@kewlgeek555

Answer 2

@ganeshie8

Answer 3

factor first two terms
factor last two terms

Answer 4

x^3 + x^2 – 4x – 4
--------- -------

Answer 5

wats the GCF of first two terms ?

Answer 6

x^2 right?

Answer 7

Yes !!
pull it out

Answer 8

x^3 + x^2 – 4x – 4

x^2(x + 1) - 4x - 4
-------

Answer 9

now look at last two terms.
wats the GCF ?

Answer 10

4

Answer 11

yup

Answer 12

x^3 + x^2 – 4x – 4

x^2(x + 1) - 4x - 4

x^2(x + 1) - 4(x + 1)
---------- --------

Answer 13

now look at those two groups.
is there anything common ?

Answer 14

(x + 1) is the common right ?

Answer 15

yes

Answer 16

so u can pull it out

Answer 17

x^3 + x^2 – 4x – 4

x^2(x + 1) - 4x - 4

x^2(x + 1) - 4(x + 1)

(x+1)(x^2-4)

Answer 18

are we done ?
or can we still factor it ?

Answer 19

they both have x

Answer 20

notice that x^2-4 = x^2-2^2

and use the identity :
a^2-b^2 = (a+b)(a-b)

Answer 21

x^3 + x^2 – 4x – 4

x^2(x + 1) - 4x - 4

x^2(x + 1) - 4(x + 1)

(x+1)(x^2-4)

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

(x+2)(x+2)(x-2)

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

Answer 22

now its completely factored.
see if it makes more or less sense

Answer 23

thank you, you put it very simply

Answer 24

glad it mad sense :) u wlc :)

Answer 25

*made