Question

if -1 and -3/2 are the zeros of polynomial
$2x {}^{3} + {x}^{2} - 7x - 6$
Find the third factor.

Answer 1

EQUATION ( 2x³ + x² - 7x - 6 ) is zero for x = -1 &
x = -3/2

x + 1 = 0 & x + (3/2) = 0
x + 1 = 0 & 2x + 3 = 0

Multiplying both the equations
(x + 1) (2x + 3) = 0
2x² + 5x + 3 = 0

Now by dividing equation ( 2x³ + x² - 7x - 6 ) by equation ( 2x² + 5x + 3 ) , quotient will be equal to zero

Division is given in the picture .

After division
x - 2 = 0
x = 2

THIRD FACTOR OF THIS EQUATION IS 2