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Every polynomial defines a function, often called P. Any value of x for which P(x) = 0 is a root of the equation and a zero of the function. So,
P(x) = x^2 - x - 35
0 = X^2 - x - 35 or,
x^2 - x - 35 = 0
We can factor this equation as (x - r1)(x - r2) = 0. Let's find r1 and r2:
x^2 - x - 35 = 0 add 35 to both sides;
x^2 - x = 35 ad to both sides 1/4 in order to complete the square;
x^2 - x + 1/4 = 35 + 1/4
(x - 1/2)2 = 141/4
x - 1/2 = +,- square root of 141/4
x = 1/2 +,- 1/2(square root of 141)
x = (1 + square root of 141)/2 or
x = (1 - square root of 141)/2
So the factorization is:
[x - (1 + square root of 141)/2 ] [x - (1 - square root of 141)/2 ]
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