Theory question 101
PolynomialsIf f(x) = 6x3 + 13x2 + 2x − 5 and f(−1) = 0, find the factors of f(x).
Show the model answer
Model answer
f(−1) = 0, so (x + 1) is a factor
Divide: f(x) = (x + 1)(6x2 + 7x − 5)
6x2 + 7x − 5 = (2x − 1)(3x + 5)
Factors: (x + 1), (2x − 1) and (3x + 5)
Explanation
Use the given root to find one factor, then factorise the quadratic quotient.