How do you factor #3x^2+36x+105#?

2 Answers
May 18, 2018

Answer:

#3(x+5)(x+7)#

Explanation:

#"take out a "color(blue)"common factor "3#

#=3(x^2+12x+35)#

#"to factor the quadratic"#

#"the factors of + 35 which sum to + 12 are + 5 and + 7"#

#=3(x+5)(x+7)#

May 18, 2018

Answer:

#3(x+5)(x+7)#

Explanation:

A quadratic polynomial can be factored if it has zeroes: you can write

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

if #x_1# and #x_2# are solutions of the polynomial. So, let's see if our polynomial has solutions: the quadratic formula yields

#x_{1,2} = \frac{-36\pm\sqrt(1296 - 1260)}{6} = \frac{-36 \pm 6}{6}#

So,

#x_1 = \frac{-36+6}{6} = -5#

#x_2 = \frac{-36-6}{6} = -7#

Thus, #3x^2+36x+105 = 3(x+5)(x+7)#