Question

[8.02] Determine the factors of 15x2 + 3xy + 10x + 2y.

(3x + 2)(5x + y)

(5x + y)(2x + 3)

(3x + y)(5x + 2)

(5x + 3)(2x + y)

Answer 1

Help me please and thank you

Answer 2

Let's take the common factors from \(15x^2\) and \(3xy\)
first:
$$
15x^2+3xy=3x(5x^2+y)
$$
Do you see that?

Answer 3

Next, let's find the common factors of 10x and 2y.

Do you see it?

Answer 4

yes

Answer 5

tell me

Answer 6

i see it but how do i solve it

Answer 7

Correction to the above:
$$
15x^2+3xy=3x(5x+y)
$$
For the next two terms, we have:
$$
10x+2y=2(5x+y)
$$

Put it all together then we get
$$
3x(5x+y)+2(5x+y)
$$
Do you see the next step?

Answer 8

yea

Answer 9

We have something in common with the \(3x \) and the 2:

It's the \( 5x+y\) term.

So bring out the \( 5x+y\) term and we have:

$$
(5x+y)(3x+2)
$$

That it!

Answer 10

oh ok thank you

Answer 11

If you can find like terms between any two pairs, try it and then see if the next two terms have the same factors in common. If that doesn't work, there are other things to try.

Answer 12

You're welcome and Good luck!