Answer to Question #22486 in Trigonometry for Kristen Woods

Question

Solve the given equations by factoring.

8a. a^8=9a^6

8b. x^3-5x^2-4x+20=0

Answer 1

8a. a^8=9a^6
a^8-9a^6=0
a^6(a^2-9)=0
a^6=0 or a^2-9=0
From first equation a=0 and from second equation a=3 or a=-3
Answer: a = -3, 0, 3

8b. x^3-5x^2-4x+20=0
We grouped x^3 with -4x and -5x^2 with 20
Then we have:
(x^3-4x)-(5x^2-20)=0
x(x^2-4)-5(x^2-4)=0
(x^2-4)(x-5)=0
Then x^2-4=0 or x-5=0
x=-2, 2 or x=0
Answer: x=-2, 0, 2