Question

show that x^2-3 is a factor of 2x^4+3x^3-2x^2-9x-12

Not by actual division method.
Spam answers are not allowed.

copying answers are deleted​

Answer 1

If x² - 3 is a factor of p(x) then the polynomial must be equal to 0 after putting value of x.

So,

x² - 3 = 0

x² = 3

x = √3

Now, putting value of x in p(x)

2x⁴ + 3x³ - 2x² - 9x - 12

x = √3

2(√3)⁴ + 3(√3)³ - 2(√3)² - 9(√3) - 12 = 0

18 + 9√3 - 6 - 9√3 - 12 = 0

18 - 6 - 12 = 0

12 - 12 = 0

0 = 0

Hence, Proved