Question

Need this explained? What are the factored forms of the following expressions?
d^2+12d+32
d^2-12d+32
x^2-2-42
d^2-18d+80
x^2+3yx-4y^2

Answer 1

#1-5

Answer 2

@TuringTest i only need help with the last one can you help me out?

Answer 3

x^2+3yx-4y^2
(ax + by)(cx + dy)
think of the possibles factors for the coefficient of x and y
for x you have either a=c=1 or a=c=-1
for y you have
b=1, d=-4
b=-1, d=4
b=2, d=-2
b=-2, d=2
b=4, d=-1
b=-4, d=1
noticing that the cross term has a coefficient of 3 should suggest that b=+/-2, d=+/-2 are unlikely
try the other potential factors until they foil out properly

Answer 4

ruling out the middle two options, as I said, there are only 8 possibilities total. Just exhaust the possibilities.

Answer 5

oh wow thats a lot to figure out

Answer 6

not really...
(x-4y)(x+y)=?
(-x-4y)(-x+y)=?
(x+4y)(x-y)=?
(-x+4y)(-x-y)=?
.
.
.
that's already half the possibilities right there

Answer 7

so if im doing this right the first number will be x-4?

Answer 8

no, it's got to have a y in it

Answer 9

oh sorry for got to put y at the end

Answer 10

so it would be x-4y?

Answer 11

right

Answer 12

then its x+y?

Answer 13

nope its x-y. thanks for your help man i appreciate it!