Question

Which of the following is equivalent to (x+3)(4x^2+5) ?

Answer 1

Answer:

c. (x+3)(4x2)+(x+3)(6)   (see the original solution on the bottom)

Step-by-step explanation:

Solve for x over the real numbers:

(x + 3) (4 x^2 + 5) = 0

Split into two equations:

x + 3 = 0 or 4 x^2 + 5 = 0

Subtract 3 from both sides:

x = -3 or 4 x^2 + 5 = 0

Subtract 5 from both sides:

x = -3 or 4 x^2 = -5

Divide both sides by 4:

x = -3 or x^2 = -5/4

x^2 = -5/4 has no solution since for all x on the real line, x^2 >=0 and -5/4<0:

Answer:  x = -3

____________________________

Solve for x over the real numbers:

2 (x + 3) (2 x^2 + 3) = 0

Divide both sides by 2:

(x + 3) (2 x^2 + 3) = 0

Split into two equations:

x + 3 = 0 or 2 x^2 + 3 = 0

Subtract 3 from both sides:

x = -3 or 2 x^2 + 3 = 0

Subtract 3 from both sides:

x = -3 or 2 x^2 = -3

Divide both sides by 2:

x = -3 or x^2 = -3/2

x^2 = -3/2 has no solution since for all x on the real line, x^2 >=0 and -3/2<0:

Answer:  x = -3