Question

I can't figure out how to do this problem: One of the factors of 3x^2+x is:

Answer 1

There are two terms: 3x^2 and x
The facors of the two terms are:
3x^2 = 3 * x * x
x = x
Which factor do both terms have in common?

Answer 2

tahe the common term x(3x+1)

Answer 3

i'm so lost....i don't know how to do the problem at all, i literally have nothing to go from...

Answer 4

What do 3 * x * x and x have in common?

Answer 5

ok, i see how the x is in the first term and x is the second term, so they are equal.
so all i have to do is find what is the same factor of the terms?

Answer 6

So the x ic common to both.

Answer 7

That's one of the factors. The question is answered.

Answer 8

Since 3x^2 + x = x(3x + 1), x is one of the factors and 3x + 1 is the other factor.

Answer 9

so in the problem x^2-9, x *x would be a factor and x-9 would be the other, so they would have x in common too?

Answer 10

x^2 - 9 is a special type of factoring called the difference of two squares.
a^2 - b^2 = (a+ b)(a - b)

Answer 11

There is no x in common because the second term, -9, has no x.

Answer 12

so i should've factored it as x*x and just -9 which have nothing in common ..?..

Answer 13

In your case, a = x, and b = 9
x^2 - 9 = x^2 - 3^2. As you can see it's the difference of two squares. x^2 is the square of x, and 9 is the square of 3, so
x^2 - 9 = (x + 3)(x - 3)

Answer 14

oh wow. i need to study more because this does't make enough sense to me. i really appreciate your help, though!

Answer 15

i just don't understand how (x+3) became part of the answer

Answer 16

When you use FOIL to multiply out (x +3)(x - 3), you do get x^2 - 9.

Answer 17

i can do the FOIL work to check the answer, just can figure out how the (x+3) came to be

Answer 18

When you multiply two binomials that follow this pattern,
(a + b)(a - b), the middle term of the soultion cancles out and you get just a^2 - b^2.