Question

What happens
happens if you factor
out 3x from
from 6x2-12x? Describe your answer​

Answer 1

The distributive property:
a
(
b
+
c
)
=
a
b
+
a
c
a(b+c)=ab+aca, left parenthesis, b, plus, c, right parenthesis, equals, a, b, plus, a, c

To understand how to factor out common factors, we must understand the distributive property.
For example, we can use the distributive property to find the product of
3
x
2
3x
2
3, x, squared and
4
x
+
3
4x+34, x, plus, 3 as shown below:

3x2(4x+3)=3x2(4x)+3x2(3)
Notice how each term in the binomial was multiplied by a common factor of
3
x
2
3x
2
start color #01a995, 3, x, squared, end color #01a995.
However, because the distributive property is an equality, the reverse of this process is also true!

3
x
2
(
4
x
)
+
3
x
2
(
3
)
=
3
x
2
(
4
x
+
3
)
3x
2
(4x)+3x
2
(3)=3x
2
(4x+3)
If we start with
3
x
2
(
4
x
)
+
3
x
2
(
3
)
3x
2
(4x)+3x
2
(3)3, x, squared, left parenthesis, 4, x, right parenthesis, plus, 3, x, squared, left parenthesis, 3, right parenthesis, we can use the distributive property to factor out
3
x
2
3x
2
start color #01a995, 3, x, squared, end color #01a995 and obtain
3
x
2
(
4
x
+
3
)
3x
2
(4x+3)3, x, squared, left parenthesis, 4, x, plus, 3, right parenthesis.
The resulting expression is in factored form because it is written as a product of two polynomials, whereas the original expression is a two-termed sum.