Question

if (x+5)(x+p)=x^2+2x+k, then ?

Answer 1

first: use FOIL to multiply out the stuff on the left side

Answer 2

then what

Answer 3

what did you get?

Answer 4

x^2+2x+k=x^2+10p+5x

Answer 5

FOIL means first, outer, inner last
(x+5)(x+p)
First: x*x or x^2
outer: x*p or px
inner: 5x
last: 5p

x^2 +px+5x+5p
factor out the x to get
x^2 +(p+5)x +5p

set this equal to the other quadratic
x^2 +(p+5)x +5p = x^2+2x+k

now match coefficients: the "numbers" in front of the x must be equal.
p+5 = 2
and 5p must equal k

Answer 6

then k=-2x^2-7x-xp-5p

Answer 7

it might not be obvious but when you have
x^2 +(p+5)x +5p = x^2+2x+k
it must be that
x^2= x^2
(p+5)x = 2x
5p= k
for this equation to always be true

Answer 8

can you find p?

Answer 9

yes

Answer 10

once you find p, you can find k:
5p= k