Question

factorise question 33 35 37​

Answer 1

33: we need to factorize.

(x-1)(x-3)(x-5)(x-7)-64

we can buy the rational root theorem, see that there are no root of this polynomial. Next observation is that if the first part of the polynomial is a square we can rewrite the whole polynomial as the difference of two squares. But it turns out that the first part of the polynomial is not a square. However, we can note that

(x-1)(x-7)=(x2)-8x+7

(x-1)(x-7)=(x2)-8x+15

(x-3)(x-5)=(x2)-8x+15

therefore, letting

(x2)-8x+7=p(x2)-8x+7=p, we can rewrite the given polynomial as

p(p+8)-64=p 2+8p-64

now it is the the factorisable

hope it helps