Question

15. Without actual division prove that x^4+2x^3-2x^2+2x-3 is exactly divisible by x ^2+ 2x-3.​

Answer 1

Step-by-step explanation:

To prove this,we have to use the factor theorem.

So we need to factorize the divisor.

so,

x^2+2x-3=

x^2-1x+3x-3

=x(x-1)+3(x-1)

=(x-1)(x+3)

therefore,

if 1 and 3 are the root of the dividend,then the polynomial is exactly divisible

since these are the roots of the polynomial,the divisor is divisible by the dividend

have a nice day!