Answer:
(5x+6)(x+7)
Explanation:
Factor the expression by grouping. Expression needs to be rewritten as 5x
2 +ax+bx+42.
To find a and b
a+b=41
ab=5×42=210
Since ab is positive, a and b have the same sign. List all such integer pairs that give product 210.
1,210
2,105
3,70
5,42
6,35
7,30
10,21
14,15
Calculate the sum for each pair.
1+210=211
2+105=107
3+70=73
5+42=47
6+35=41
7+30=37
10+21=31
14+15=29
The solution is the pair that gives sum 41.
a=6
b=35
Rewrite 5x
2 +41x+42 as (5x^2 +6x)+(35x+42).
Factor out x in the first and 7 in the second group.
x(5x+6)+7(5x+6)
Factor out common term 5x+6 by using distributive property.
(5x+6)(x+7)