Question

Fill in the blank to make the expression a perfect square

Answer 1

v2+4v +

Answer 2

Take half of \(\Large {\color{red}{4}}\) in \(\Large v^2 + {\color{red}{4}}v + \) to get what?

Answer 3

2

Answer 4

?

Answer 5

now square that result

Answer 6

4

Answer 7

so 4 goes in the blank
\[\Large v^2 + 4v + \underline{ \ \ 4 \ \ }\]

Answer 8

The polynomial
\[\Large v^2 + 4v + 4\]
is a perfect square which factors to \(\Large (v+2)^2\)

Answer 9

really?

Answer 10

o ok i get it

Answer 11

yeah let's try another example

say I gave you this

v^2 + 10v + ________

Answer 12

step 1) take half of 10 (the second coefficient)

step 2) square the result from step 1

what do you get?

Answer 13

25

Answer 14

yep so
v^2 + 10v + ________
turns into
v^2 + 10v + 25

Answer 15

v^2 + 10v + 25 would factor to (v+5)^2

notice how the 10 cuts in half to 5

Answer 16

yeah i get it now . thank you so much :)

Answer 17

make more sense now

Answer 18

you're welcome