Question

Find all rational zeroes of P(x) = x³ -7x+6​

Answer 1

Answer:

Solve for x:

x^3-7 x+6 = 0

The left hand side factors into a product with three terms:

(x-2) (x-1) (x+3) = 0

Split into three equations:

x-2 = 0 or x-1 = 0 or x+3 = 0

Add 2 to both sides:

x = 2 or x-1 = 0 or x+3 = 0

Add 1 to both sides:

x = 2 or x = 1 or x+3 = 0

Subtract 3 from both sides:

Answer: | x = 2 or x = 1 or x = -3