Question

The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 4z^2+2z square meters. Factor this polynomial to find possible expressions for the length and width of the wall. (Assume the factors are polynomials.) If z=4 what would the length and width be?

Answer 1

please help me understand this.

Answer 2

if z=4, then what is the area?

Answer 3

I'm not sure

Answer 4

4z^2+2z

plug in 4 for z

Answer 5

264 ?

Answer 6

no. 4(4)^2=4*16=64
2*4=8
64+8=72

Answer 7

oh, I squared it again 16^2+8,
I get it

Answer 8

now the question says to factor the polynomial. can you do that?

Answer 9

No, how would I do that?

Answer 10

ok. we need 2 different numbers which when multiplied together equals 72.
so we factor 4z^2+2z by "taking out" of each term the common factors. what do you think the common factors are?

Answer 11

2 and 4?

Answer 12

getting close.

2 is common to each of 4z^2 and 2 z. 4 is not common to both.
but there is something else that they share in common.

Answer 13

1?

Answer 14

z is comon to both.

Answer 15

oh, ok. both of them have z

Answer 16

so "take out" 2z from both terms as follows
2z(?+?)=4z^2+2z

Answer 17

(?+?)=4z^2 like this?

Answer 18

like this
2z(2z+1)

Answer 19

oh ok

Answer 20

so 2z is one number and 2z+1 is the other number. if z=4, what are the 2 numbers and if you multiply them together do you get 72?

Answer 21

8 and 9

Answer 22

yup. good job!

Answer 23

thanks alot!

Answer 24

you are welcome!