1) 15x^2+4x-4< or = 0 solve by Algebraic method ?
Answers
Algebra Factoring Completely
1 Answer
Tony B
May 8, 2016
Answer:
(
3
x
+
2
)
(
5
x
−
2
)
Explanation:
It is a matter of spotting possible combinations and trying them out. They can be tried out on paper or in your head.
Factors of 15
→
{1,15} ; {3,5}
Factors of 4
→
{1,4} ; {2,2}
Cross link factors of 4 with factors of 15
'......................................................................
Consider: {1,4} linked to {1,15}
(
1
×
15
)
−
(
4
×
1
)
=
11
So this is no good for obtaining
4
x
'........................................................................
Consider: {2,2} linked to {1,15}
(
2
×
15
)
−
(
2
×
1
)
=
28
So this is no good for obtaining
4
x
'.......................................................................
Consider: {1,4} linked to {3,5}
(
3
×
4
)
−
(
1
×
5
)
=
7
So this is no good for obtaining
4
x
'..............................................................
Consider: {2,2} linked to {3,5}
(
2
×
5
)
−
(
2
×
3
)
=
4
this is the combination we need
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(
3
x
+
2
)
(
5
x
−
2
)
Explanation:
It is a matter of spotting possible combinations and trying them out. They can be tried out on paper or in your head.
Factors of 15
→
{1,15} ; {3,5}
Factors of 4
→
{1,4} ; {2,2}
Cross link factors of 4 with factors of 15
'......................................................................
Consider: {1,4} linked to {1,15}
(
1
×
15
)
−
(
4
×
1
)
=
11
So this is no good for obtaining
4
x
'........................................................................
Consider: {2,2} linked to {1,15}
(
2
×
15
)
−
(
2
×
1
)
=
28
So this is no good for obtaining
4
x
'.......................................................................
Consider: {1,4} linked to {3,5}
(
3
×
4
)
−
(
1
×
5
)
=
7
So this is no good for obtaining
4
x
'..............................................................
Consider: {2,2} linked to {3,5}
(
2
×
5
)
−
(
2
×
3
)
=
4
this is the combination we need
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(
3
x
+
2
)
(
5
x
−
2
)