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10 votes
10 votes
Write this trinomial in factored form.
5a2 - 3a - 14

User Niklas Gustavsson
by
3.1k points

1 Answer

29 votes
29 votes

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)

User Maverick Meerkat
by
3.4k points
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