find the factor of 2x²+11x+15
Answers
Step-by-step explanation:
To factor this expression we will need to factor each of the terms individually so that when we reverse the factorization, the terms will re-multiply into the given expression.
Given:
2
x
2
+
11
x
+
15
Because we start out with
x
2
we know we will end up with two brackets:
(
...
)
(
...
)
We know that each bracket will need an
x
inside:
(
x
...
)
(
x
...
)
In this case we can see that one of the
x
terms will need to be multiplied by 2 since we start with
2
x
2
. So
(
2
x
...
)
(
x
...
)
We know that each bracket will need a numerical factor. In this case the number to be factored is:
15
=
(
15
)
(
1
)
=
(
3
)
(
5
)
=
(
5
)
(
3
)
So we can write in:
(
2
x
...
15
)
(
x
...
1
)
=
(
2
x
...
3
)
(
x
...
5
)
=
(
2
x
...
5
)
(
x
...
3
)
But we need to have factors that when multiplied by
x
will add or subtract to result in the central term of the expression - in this case
11
x
.
We can see that
2
⋅
3
=
6
and
5
⋅
1
=
5
will result in
11
when added. This indicates both numeric terms need to be
+
.
The given expression also agrees with the double
+
, because both signs are
+
.
Then we can write:
2
x
2
+
11
x
+
15
=
(
2
x
+
5
)
(
x
+
3
)
To check for correctness, simply re-multiply the answer to result in the given expression.
Answer:
(x+3) (2x+5)
Step-by-step explanation:
2x^2 + (6+5)x + 15
=2x^2 + 6x + 5x +15
=2x(x+3) +5(x+3)
=(x+3) (2x+5)