Question

Write g(x) = 2x³ - 9x² + 12x - 4 in factored form​

Answer 1

Answer:

We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12

Fir.st equate 2x-3 to 0 and find value of x.

2x - 3 = 0

⇒ 2x = 3

⇒ x = 3/2

If x=3/2 is a root of the polynomial, then (2x-3) is a factor.

at x=3/2, value of polynomial is

2(3/2)³ - 9(3/2)² + 3/2 + 12

= 2×(27/8) - 9×(9/4) + 3/2 + 12

= 27/4 - 81/4 + 3/2 + 12

= (27 - 81 + 6 + 48)/4

= (81-81)/4

= 0

So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.