Answer:
b: -5
Explanation:
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as 3x
2
+ax+bx−5. To find a and b, set up a system to be solved.
a+b=14
ab=3(−5)=−15
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −15.
−1,15
−3,5
Calculate the sum for each pair.
−1+15=14
−3+5=2
The solution is the pair that gives sum 14.
a=−1
b=15
Rewrite 3x
2
+14x−5 as (3x
2
−x)+(15x−5).
(3x
2
−x)+(15x−5)
Factor out x in the first and 5 in the second group.
x(3x−1)+5(3x−1)
Factor out common term 3x−1 by using distributive property.
(3x−1)(x+5)
To find equation solutions, solve 3x−1=0 and x+5=0.
x=
3
1
x=−5