Answer:
(a-2) (5a+7)
Explanation:
Factor the expression by grouping. First, the expression needs to be rewritten as 5a^2 +pa+qa−14. To find p and q, set up a system to be solved.
p+q=-3
pq= 5 (-14) = -70
Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −70.
1,-70
2,-35
5,-14
7,-10
Calculate the sum for each pair.
1-70=-69
2-35=-33
5-14=-9
7-10=-3
The solution is the pair that gives sum −3.
p=-10
q=7
Rewrite 5a^2 −3a−14 as (5a^2 −10a)+(7a−14).
(5a^2 −10a)+(7a−14).
Factor out 5a in the first and 7 in the second group.
5a (a−2)+7(a−2)
Factor out common term a−2 by using distributive property.
(a−2)(5a+7)