Question

show that: 2x-3 is a factor of x+2x^3-9x2+12​

Answer 1

Step-by-step explanation:

p(x) = x+2x³-9x²+12 = 2x³-9x²+x+12

g(x) = 2x-3

now, g(x) = 0

⇒2x-3 = 0

⇒2x = 3

⇒x = $\frac{3}{2}$

Now, p($\frac{3}{2}$) = 2×$(\frac{3}{2})^3$-9×$(\frac{3}{2})^2$+$\frac{3}{2}$+12

= 2×($\frac{27}{8}$)-9×($\frac{9}{4}$)+$\frac{3}{2}$+12

= $\frac{27}{4}$-$\frac{81}{4}$+$\frac{3}{2}$+12

= $\frac{27-81+6+48}{4}$

= $\frac{0}{4}$ = 0

Since, p($\frac{3}{2}$) = 0

Therefore, 2x-3 is a factor of x+2x³-9x²+12 or 2x³-9x²+x+12