Algebra 2 test tomorrow solve by factoring

Question

How would i solve 8x^4-10x^2+3=0? Thanks for the help

Answer 1

8x^4 - 10x^2 + 3 = 0

Just for kicks, let's try completing the square:

8x^4 - 10x^2 = -3

x^4 - 5/4x^2 = -3/8

x^4 - 5/4x^2 + 25/64 = -3/8 + 25/64

(x^2 - 5/8)^2 = -3/8 + 25/64 = 1/64

x^2 - 5/8 = ±1/8

x^2 = 6/8, 4/8

x = ±√6/8, ±√4/8

= ±(√3)/2, ±(√2)/2

Answer 2

The factoring method we would need to use is called quadratic method. Even though this is not a quadratic it fits the mold ay² + by + c where y = x².

I would tell my students to think about factoring the quadratic 8y² - 10y + 3 and then substitute x² for y at the end.

8y² - 10y + 3 = (4y - 3)(2y - 1) and when you substitute you get (4x² - 3)(2x² - 1). This is as far as you can go with factoring, but to find the solutions we can set each factor equal to zero and solve by taking square roots.

4x² - 3 = 0

4x² = 3

x² = 3/4

x = ±√3/2

2x² - 1 = 0

2x² = 1

x² = 1/2

x = ±√2/2

So the four solutions are ±√3/2 and ±√2/2