Is it possible to factor #y=x^4 - 13x^2 + 36#? If so, what are the factors?
3 Answers
Explanation:
a quadratic in u
both brackets are differences of squares
Explanation:
Explanation:
#"using the "color(blue)"substitution "u=x^2#
#rArrx^4-13x^2+36=u^2-13u+36#
#"the factors of + 36 which sum to - 13 are - 9 and - 4"#
#rArru^2-13u+36=(u-9)(u-4)#
#"change u back into terms of x gives"#
#(x^2-9)(x^2-4)#
#"both "x^2-9" and "x^2-4" are "color(blue)"difference of squares"#
#"which factorise, in general as"#
#•color(white)(x)a^2-b^2=(a-b)(a+b)#
#rArrx^2-9=(x-3)(x+3)#
#rArrx^2-4=(x-2)(x+2)#
#rArrx^4-13x^2+36=(x-3)(x+3)(x-2)(x+2)#