Question

factor the perfect square trinomial completely.
z^4-14z^2+49

Answer 1

do you know how to factor trinomials?

Answer 2

in quadratic form?

Answer 3

not really o.o

Answer 4

well you know a perfect square trinomial factors into two binomials:
\[(x + y)(x + y) \]
the signs may vary.

do you know this much?

Answer 5

yes

Answer 6

okay then let's get started
disregard the variables for now, and find two numbers who's product is +49
and who's sum is -14

Answer 7

-7 and -7

Answer 8

okay you know that your constants in the binomial are going to be -7 and -7
so your equation will look something like this
(x-7)(x-7) right?

now all we need to do is find out what your x's are

Answer 9

the leading variable is \[z^4\]
and the middle variable is \[z^2\], if you square \[z^2\] you get \[(z^2)^2\]

Answer 10

which equals \[z^4\], so your equation is
\[(z^2 -7)(z^2 - 7)\]

Answer 11

or \[(z^2 - 7)^2\]

Answer 12

so when i solve these, i should solve the last term first?

Answer 13

what do you mean "last term first"?

Answer 14

solve for 49

Answer 15

the last term is "c" if you remember the form of a quadratic equation:
\[ax^2 +bx + c\]

Answer 16

well if you remember, to solve these types of equations, you need to find two numbers whose product is "c" (+/- depending on the sign before it) and whose sum is b (also +/- depending on the sign before it)

Answer 17

you don't really solve for the last term, you use it as a basis, since you'll only get half of the answer, basically

Answer 18

and your variable would just be whatever the middle variable is (in ur case it was z^2) just make sure it is in quadratic form (that is, \[\sqrt{x^2} = x\]

Answer 19

in ur case:
\[\sqrt{z^4} = z^2\]

Answer 20

and that holds true for the middle variable being your leading variable in the binomials in your answer.