Question

verify that X - 1, x minus 2 and 2 x minus 1 are the factors of the polynomial 2 x cube minus 5 x square + X + 2​

Answer 1

Verification:

p(x) = 2x³ - 5x² + x +2

1. To find the zero,

x-1 = 0

x = 1

p(1) = 2(1) - 5(1) + (1) + 2

= 2 - 5 + 1 + 2

= 5 - 5

= 0

Hence, proved.

2. To find the zero,

x - 2 = 0

x = 2

p(2) = 2(2)³ - 5(2)² + 2 + 2

= 16 - 20 + 2 + 2

= 20 - 20

= 0

Hence, proved.

3. To find the zero,

2x -1 = 0

2x = 1

x = 1/2

p(1/2) = 2(1/2)³ - 5(1/2)² + 1/2 + 2

= 2(1/8) - 5/4 + 1/2 + 2

= 1/4 - 5/4 + 1/2 + 2

= 3/4 - 5/4 + 2

= -1/2 + 2

= (4-1)/2

= 3/2

=1.5

(2x-1) is not a factor of p(x).