How do you factor: #y= 9x^4 - 12x^2 +4 #?
1 Answer
Apr 16, 2017
Explanation:
This function can be expressed as a
#color(blue)"quadratic function"#
#"use the substitution " u=x^2" and express y as"#
#y=9u^2-12u+4# Now factorise as a quadratic.
#ac=9xx4" and " b=-12# Consider the product of the factors which give 36 and sum to
- 12
#"these are " -6" and " -6#
#rArry=9u^2-6u-6u+4#
#" Factorise by grouping"#
#y=color(red)(3u)(3u-2)color(red)(-2)(3u-2)#
#"factor out the " color(blue)"common factor" " of " (3u-2)#
#rArry=(3u-2)(color(red)(3u-2))=(3u-2)^2#
#"change u back into terms of x"#
#rArry=(3x^2-2)^2#
