Polynomials Exercises

Find the possible rational roots of y = 3x⁵ + 2x⁴ – x³ – x² + 6x + 16

Hint

The constant's factors are ±1, ±2, ±4, ±8, and ±16. The leading term's factors are ±1 and ±3.

Find the possible rational roots of f(x) = x⁴ − 10x³ + 37x²− 60x + 36

Hint

The constant's factors are ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, and ±36. The leading term's factors are ±1.

Could the polynomial y = 5x³ − 10x² + 17x + 28 have (x – 5) as a factor?

Hint

The factors of the constant term are on top, and the factors of the leading term are on bottom.

Could the polynomial y = x⁴ + x³ + x² – x – 2 have a zero between 0 and 1?

Hint

The factors of the constant term are ±1 and ±2, and the factors of the leading term ±1.

Find all of the roots of y = 2x³ + 4x² + 5x + 10.

Hint

Try x = -2.