Factor completely 3x2 + 9x − 54.l

Question

asked Mar 21, 2018 190k views

2 Answers

Hanugm · Answer 1 · 2018-03-27T04:20:36+0000

Answer: The complete factorization of the given expression is
3(x-3)(x+6).

Step-by-step explanation: We are given to factor completely the following quadratic expression :

$E=3x^2+9x-54\\\\\Rightarrow E=3(x^2+3x-18)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To completely factor expression (i), we need two integers with sum 3 and product -18. Those two integers are 6 and -3.

The complete factorization of expression (i) is as follows :

$E\\\\=3(x^2+3x-18)\\\\=3(x^2+6x-3x-180)\\\\=3(x(x+6)-3(x+6))\\\\=3(x-3)(x+6).$

Thus, the complete factorization of the given expression is
3(x-3)(x+6).