Can someone please help me with problem #1 of the Rational Roots Theorem and Factoring/Solving worksheet? Please show your work.
Directions: State the factors of the constant, factors of the leading coefficient, and possible rational roots in each function. Then factor each and find all roots.
1. Find factors of the constant term (-1): ±1 2. Find factors of the leading coefficient (5): ±1, ±5 3. Possible rational roots: ±1/1, ±1/5 4. Use synthetic division with each possible root. 5. Since f(1) = 0, x = 1 is a root. 6. Factor polynomial using synthetic division with x = 1 as a root: (x - 1)(5x^2 - 6x + 1) 7. Solve 5x^2 - 6x + 1 = 0 to find remaining roots: (5x - 1)(x - 1) 8. Remaining roots: x = 1/5, x = 1 9. Roots of f(x) = 5x^3 - 11x^2 + 7x - 1 are x = 1, x = 1/5, and x = 1.
