2017 · Q3
What are the factors of x³+4x²-11x-30 ?
Elementary MathematicsAlgebra
- A(x-2),(x+3) and (x+5)
- B(x+2),(x+3) and (x-5)
- C(x+2),(x-3) and (x+5)
- D(x+2),(x-3) and (x-5)
Explanation
Test possible linear factors with the factor theorem. p(−2) = −8+16+22−30 = 0, so (x+2) is a factor; p(3) = 27+36−33−30 = 0, so (x−3) is a factor; p(−5) = −125+100+55−30 = 0, so (x+5) is a factor. A cubic has exactly three linear factors, giving (x+2)(x−3)(x+5). Hence option (C).