Question

Without any 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:

Without actual division prove that x4 + 2x3 - 2x2 + 2x - 3 is exactly divisible by x2 + 2x - 3. Hence by converse of factor theorem, (x + 3) is a factor of p(x). Hence by converse of factor theorem, (x - 1) is a factor of p(x). ⇒ p(x) is exactly divisible by (x2 + 2x - 3).

Answer 2

$\sf\fbox\red{Answer:-}$

Without actual division prove that x4 + 2x3 - 2x2 + 2x - 3 is exactly divisible by x2 + 2x - 3. Hence by converse of factor theorem, (x + 3) is a factor of p(x). Hence by converse of factor theorem, (x - 1) is a factor of p(x). ⇒ p(x) is exactly divisible by (x2 + 2x - 3)