118k views
5 votes
Prove that the expression 2x(x–6)–3(x2–4x+1) is negative for all values of x.

1 Answer

3 votes
Simplify the following:
2 x (x - 6) - 3 (x^2 - 4 x + 1)

2 x (x - 6) = 2 x^2 - 12 x:
2 x^2 - 12 x - 3 (x^2 - 4 x + 1)

-3 (x^2 - 4 x + 1) = -3 x^2 + 12 x - 3:
-3 x^2 + 12 x - 3 + 2 x^2 - 12 x

Grouping like terms, 2 x^2 - 3 x^2 + 12 x - 12 x - 3 = (2 x^2 - 3 x^2) - 3 + (-12 x + 12 x):
(2 x^2 - 3 x^2) - 3 + (-12 x + 12 x)

2 x^2 - 3 x^2 = -x^2:
-x^2 - 3 + (-12 x + 12 x)

12 x - 12 x = 0:
-x^2 - 3

Factor -1 out of -x^2 - 3:
Answer: -(x^2 + 3)
User Qaziqarta
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories