4x4 + 13x2 + 36 is a quadratic in x2.
The discriminant is 132 - 4*4*36 = -407.
Since the discriminant is negative, the expression has no real roots and so it cannot be factorised (in the normal sense of the term).
(x - 2)(x + 2)(x - 3)(x + 3)
36x1 13x2 12x3 9x4 6x6
x(x2 + 36)
x^(2) + 13x + 36 Factors to ( x + 9)(x + 4) When learning factoring. ;- #1 ; If the coefficient of x^(2) is '1' , as in this case. Then #2 ; Write down all the factors of 36, which are ,1,36 ' 2,18 ' 3,12 ' 4,9 ' 6,6 ; #3 ; Out of these pairs of factors, select a pair that add/subtract to '13'. #5, They are 4,9 ; 4 + 9 = 13 #6 ; Since the quadratic eq;m has positive (+) signs , then all the signs in the brackets are positive(+). When the coefficient of x^(2) is > 1, and/or the signs are different , then different techniques come into play.
x2 + 36 cannot be factored. You can only factor the difference of two squares, not the sum.
(x + 4)(x + 9)
(x + 9)(x + 4)
2(x + 6)(x + 3)
x^(2) - 13x + 36 Factors to ( x - 9)(x - 4)
6x3 - 27x2 + 3x + 36 = 3 (x - 4) (x + 1) (2x - 3)
(x - 6)(5x - 6)
(6 - 5x)(6 - 5x)