Question

Which of the following shows the factors of 5x2 + 17x + 6?
a-(5x + 1)(x + 6)
b-(5x + 2)(x + 3)
c-(5x + 3)(x + 2)
d-(5x + 6)(x + 1)

Answer 1

Hello! Welcome :)

Give me a minute to read your question ^_^

Answer 2

ok:)

Answer 3

hmm have you learned the FOIL method before?

Answer 4

no

Answer 5

That's ok :)

so the idea we can try here is called the Distributive property.
a simple version of this idea is like this:
2*7 = 14 we know is true
2*(5+2) = 2*7 = 14 we know also works
but we can also think of it as 2*(5+2) = 2*5 + 2*2 = 10 + 4 = 14 which also gets us to 14

so when working with variables, we can use this idea to make dealing with variables easier!

Answer 6

Using this idea, we can look at Option A
(5x + 1)(x+6)
it can become
= (5x + 1)*x + (5x + 1)*6
just like how the (2) in the example I gave, gets to be multiplied to both the (5) and the other (2)

Answer 7

then just like how 2*5 = 10 = 5*2
the (5x + 1)*x we see above can be written as
x*(5x + 1)

then we can apply the Distributive Property again!
x*(5x) + x*(1)

then we simplify to get
5x^2 + x


we can do the same to the other part: (5x + 1)*6
= 5x*(6) + 1*(6)
= 30x + 6

then add both parts together
(5x^2 + x) + (30x + 6)
= 5x^2 + 31x + 6

This means that Option A: (5x + 1)(x+6)
= 5x^2 + 31x + 6

but that is Not equal to 5x^2 + 17x + 6
so A is Not the answer we're looking for

Answer 8

we can do a similar process with each option to get to your final answer ^_^

Answer 9

can you just give me the answer

Answer 10

Personally, I would say that this Distributive Property thing is important and something that you will definitely have to use in a future math class.

a-(5x + 1)(x + 6) = 5x^2 + 37x + 6
b-(5x + 2)(x + 3) = 5x^2 + 17x + 6
c-(5x + 3)(x + 2) = 5x^2 + 13x + 6
d-(5x + 6)(x + 1) = 5x^2 + 11x + 6

Answer 11

so whats the answer a,b,c,or d

Answer 12

I have literally done all the work for you, compare the options with the given question
5x^2 + 17x + 6

Answer 13

is it b

Answer 14

yup :)

Answer 15

gracias:)