Given X & # 178; - 8 = 0, find X & # 178; (X & # 178; + 1) - x (X & # 178; - 1) - X-7

Given X & # 178; - 8 = 0, find X & # 178; (X & # 178; + 1) - x (X & # 178; - 1) - X-7

The answer is 65 ± 16 √ 2

Read the following materials, because (x + 3) (X-2) = x & # 178; + X-6, so (X & # 178; + X-6) (X-2) = x + 3, which shows that X & # 178; + X-6 can be divided by X-2, and also shows that the polynomial x & # 178; + X-6 has a factor of X-2. In addition, the value of polynomial X & # 178; + X-6 is 0. Answer the following questions
(1) in general, for the polynomial m of the letter X, if x = k is, the value of M is 0, then the relation between M and the formula x-k
What does it matter?
(2) it is known that x-3 can divide X & # 178; + kx-15 and find the value of K. ② it is known that x + 4 can integrate quadratic trinomial m, and if x = 3 is, the value of quadratic trinomial m is equal to 0, then find quadratic trinomial m (let the quadratic coefficient of M be 1)
I have to hand in my exercise book tomorrow

If the quotient of x2 + X-6 divided by (X-2) (x + a) is 1, then a=______ ．

∵ (X-2) (x + a) = x2 + ax-2x-2a = x2 + (A-2) x + 2a, that is, X2 + X-6 = x2 + (A-2) x + 2a, ∵ A-2 = 1, ∵ a = 3