How do you factor completely: #2x^2 + 13x + 15#?

2 Answers
Jul 22, 2015

Answer:

#2(x + 3/2)(x + 5)#

Explanation:

#ax^2 + bx + c = a(x - x_1)(x - x_2)#

#2x^2 + 13 x + 15 = 0#

#x_i = (- 13 ± sqrt{13^2 - 4 * 2 * 15}) / 4#

#x_1 = (-13 + 7)/4 = -3/2#

#x_2 = (-13 -7)/4 = -5#

Jul 23, 2015

Answer:

Factor y = 2x^2 + 13x + 15

Explanation:

I use the new AC Method to factor trinomials (Google, Yahoo Search).
#y = 2x^2 + 13x + 15 =# 2(x - p)(x - q)
Converted #y' = x^2 + 13x + 30 = #(x - p')(x - q').
Factor pairs of ac = 30 -> (2, 15)(3, 10). this sum is 13 = b.
Then, p' = 3 and q' = 10.
Then, #p = 3/2# and #q = 10/2 = 5.#
Factored form: #y = 2(x + 3/2)(x + 5) = (2x + 3)(x + 5)#