Question

2. Consider the equation 3x2 - 13x - 30 = 0.
(a) Write the factored form of the trinomial.

Answer 1

-5/3 , 6

Explanation:

Quadratic Formula is
x = -b ± √(b^2 − 4ac))/(2a)

replace the letters with the values from the equation, and plug it in.

x = -(-13) ± √((-13)^2 − 4*3(-30))/(2(3))
=
x = (13 ± 23) / 6

You may subtract or add the 13 and 23 for a valid answer, thus the two possible values are

-5/3

and

6

Answer 2

(3x + 5)(x - 6) = 0 (Assuming 3x is to the power of two 3x^2)

Explanation:

Factor out -13 from -13x

3x^2 - 13(x) - 30 = 0

Rewrite -13 as 5 plus -18

3x^2 + (5 - 18)x - 30 = 0

Apply the distributive property

3x^2 + 5x - 18x - 30 = 0

Now factor out the GCF (Greatest common factor)

To do so we will group the first two terms and last two.

(3x^2 + 5x) - 18x - 30 = 0

Then factor out the GCF from each group.

x(3x + 5) - 6(3x + 5) = 0

(3x + 5)(x - 6) = 0