How do you factor the trinomial #5x^2+7x+2#?

2 Answers
Apr 23, 2018

(x + 1)(5x + 2)

Explanation:

#y = 5x^2 + 7x + 2#.
Since a - b + c = 0, use shortcut.
The 2 real roots are: x1 = -1 and #x2 = - c/a = - 2/5#.
Therefor, the 2 factors are--> (x + 1) and #(x + 2/5)#
Factored form:
#y = a(x - x1)(x - x2)#
#y = 5( x + 1)(x + 2/5) = (x + 1)(5x + 2)#

Reminder of Shortcut.
a. If a + b + c = 0, the 2 real roots are : 1 and #(c/a)#
b. If a - b + c = 0, the 2 real roots are: - 1 and #(- c/a)#

Apr 23, 2018

#(5x+2)(x+1)#

Explanation:

#5x^2 +7x+2#

Find factors of #5 and 2# whose products add to #7#.

We can see that #5+2=7# The other factors are both #1#

#5 xx 1 + 2xx1 = 5+2=7#

#(5x+2)(x+1)#