How do you factor #7x^2 - 9x + 2#?

Question

5670 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-06T16:54:48

You find its roots and turn them into factors by equaling them to zero.

Let's find the roots using Bhaskara:

#(9+-sqrt(81-4(7)(2)))/14#

#(9+-sqrt(81-56))/14#

#(9+-sqrt25)/14#

#(9+-5)/14#

#x_1=1#, which, equaled to zero is #x-1=0#
#x_2=2/7#, which, equaled to zero is #7x-2=0#

Thus, we can factor #7x^2-9x+2# this way:

#(x-1)(7x-2)#

Answer 2 · 2015-06-06T21:56:32

#f(x) = 7x^2 - 9x + 2.#

Since (a + b + c) = 0, one factor is (x - 1) and the other is #(-c/a = -2/7)#

f(x) = (x - 1)(7x - 2)