Find all rational zeros of the polynomial Enter your answers

Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list.) P(x) = 12x^3 - 20x^2 + x + 3 Write the polynomial in factored form. P(x) =

Solution

IN THE ABOVE QUETION WE KNOW THE RATIONAL ZEROES OF THE POLYNOMIAL.WE WILL MAKE USE OF USE THE RATIONAL ROOT TEST. HERE ONE OF THE ROOTS IS X= 1/ 2 OR 2X -1 = 0

ON DIVIDING THE ABOVE POLYNOMIAL BY 2X - 1 WE GET

(12X³ - 20X² + X + 3) / (2X -1) = (6X² - 7X - 3)

OR (12X³ - 20X² + X + 3) =  (2X -1) (6X² - 7X - 3)

NOW (6X² - 7X - 3) IS AQUDRATIC EQUATION WE WILL FACTORISE IT FURTHER

(6X² - 7X - 3) = (6X² - 9X + 2X - 3)

TAKING COMMON 3X(2X - 3) +1 (2X - 3)

= (3X + 1) (2X - 3)

SO THE FACTORED FORM OF POLYNOMIAL P(x) = (2x - 1) (3x + 1) (2x - 3).