Factorization is:
[tex]5x+40=5(x+8)\\\\7x-49=7(x-7)\\\\18x+9=9(2x+1)\\\\15x-10=5(3x-2)[/tex]
Solution:
Given that we have to factor the given expressions
First expression:
5x + 40
We have to take the greatest common factor out
When we find all the factors of two or more numbers, and some factors are the same then the largest of those common factors is the Greatest Common Factor
Take G.C.F of 5 and 40
The factors of 5 are: 1, 5
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
Then the greatest common factor is 5
Factor out 5 from given expression
[tex]5x + 40 = 5(x+8)[/tex]
Second expression:
7x - 49
Similarly, take G.C.F of 7 and 49
The factors of 7 are: 1, 7
The factors of 49 are: 1, 7, 49
Then the greatest common factor is 7
Factor out 7 from given expression
[tex]7x - 49 = 7(x-7)[/tex]
Third expression:
18x + 9
Similarly, take G.C.F of 18 and 9
The factors of 9 are: 1, 3, 9
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 9
Factor out 9 from given expression
[tex]18x + 9 = 9(2x+1)[/tex]
Fourth expression:
15x - 10
Similarly, take G.C.F of 15 and 10
The factors of 10 are: 1, 2, 5, 10
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 5
Factor out 5 from given expression
[tex]15x-10 = 5(3x-2)[/tex]
Thus factorization is found
