Home > PC > Chapter 8 > Lesson 8.2.1 > Problem 8-76
8-76.
Solve x3(x + 3)4 + 2x2(x + 3)3 = 0. Hint: Let a = x + 3 and factor. Homework Help ✎
Substitute a for x + 3:
Factor:
Set each factor = 0:
Substitute (x + 3) back in the expressions and solve.
x3a4 + 2x2a3 = 0
x2a3(ax + 2) = 0
x2a3 = 0 or ax + 2 = 0
x2(x + 3)3 = 0
x2 = 0
x = 0
(x + 3)3 = 0
x = −3
ax + 2 = 0
(x + 3)x + 2 = 0
x2 + 3x + 2 = 0
(x + 2)(x + 1) = 0
x = −2; x = −1