Question

factor 16x2+40x+25 in polynomial descending order

Answer 1

What did you get for this one?

Answer 2

i dont get it

Answer 3

Alright, something to look for when you see this type of problem. Notice that the first term (16x^2) is a perfect square, and the last term (25) is also a perfect square.

Answer 4

5

Answer 5

This means you're probably going to have something like this:
\[(a+b)^2 or (a-b)^2 \]

Answer 6

Yeah. In this case, when you factor, just take the square root of 16x^2 and the square root of 25. Tell me what you get for each.

Answer 7

(16x+5)(x+5)

Answer 8

Wait wait. Just take the square root of 16x^2 and take the square root of 25. What do you get?

Answer 9

20

Answer 10

Oh god. Lol.

Answer 11

Erm, you told me the square root of 25 is 5, right?
What is the square root of 16x^2?

Answer 12

I think she/he is searching it up on google.

Answer 13

4

Answer 14

Lol, that would also be a way to go.

Answer 15

4^2 gives 16, so you're looking for 4x. (4x)(4x)=16x^2

Answer 16

So 4x is the square root of the first term, and 5 is the square root of the second term.
Our answer is just
\[(4x+5)^2\]

Answer 17

Nifty, eh?

Answer 18

Hmm, what about 40x?

Answer 19

Good question. Now this part is really important. If we have a suspicion that our answer is
\[(4x+5)^2\]we have to check it by using FOIL. We get
\[(4x+5)^2=(4x+5)(4x+5)=16x^2+20x+20x+25=16x^2+40x+25\]

Answer 20

I just wanted the kid to see the foil method. Lol.

Answer 21

Oh, lol. Sorry, I thought that was him responding. That's where we were going next anyway. I wasn't going to let him try to use the square of a binomial with just anything that happened to have perfect squares for the first and last terms.

Answer 22

Good explaining. Keep it up!