Factor the polynomial x2-x-35? - Answers

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 ] Check.