Factor y = x^4 - 5x^2 + 4 step by step please?

Science & Mathematics by Anonymous 2018-07-14 00:33:53

Social Science

9 answers

Anonymous

y = [ x^2 - 4 ] [ x^2 - 1 ] y = [ x - 2 ] [ x + 2 ] [ x - 1 ] [ x + 1 ]
Anonymous

y = x^4 - 5x^2 + 4 y = (x^2 - 4)(x^2 - 1) y = (x + 2)(x - 2)(x + 1)(x - 1)
Anonymous

x^4-5x^2+4 =(x^2)^2+(2)^2-5x^2 =(x^2+2)^2-2x^2.2-5x^2 =(x^2+2)^2-9x^2 =(x^2+2)^2-(3x)^2 =(x^2+3x+2)(x^2-3x+2)
Anonymous

y = x^4 - 5x^2 + 4 y = (x^2 - 1)(x^2 - 4) y = (x - 2) (x - 1) (x + 1) (x + 2)
Anonymous

You'd factor the right side as follows... y = x^4 - 5x^2 + 4 y = x^4 - x^2 - 4x^2 + 4 y = x^2(x^2 - 1) - 4(x^2 - 1) y = (x^2 - 4)(x^2 - 1) y = (x + 2)(x - 2)(x + 1)(x - 1). Then go from there.
Anonymous

y = (x^2-4)(x^2-1) = (x+2)(x-2)(x+1)(x-1)
Anonymous

Hint: let u = x²
Anonymous

. y = x⁴ - 5x² + 4 let t = x² y = x⁴ - 5x² + 4 y = t² - 5t + 4 y = t² - t - 4t + 4 y = t(t - 1) - 4(t - 1) y = (t - 1)(t - 4) y = (x² - 1)(x² - 4) y = (x - 1)(x + 1)(x - 2)(x + 2) ━━━━━━━━━━━━
Anonymous

http://www.wolframalpha.com/input/?i=y+%...