Question

Using Factor theorem,Show that:
Q.(x +√2) is a factor of (2√2x² + 5x + √2)​

Answer 1

Let, 2√2x^2+5x+√2 be f(x) and it be divided by (x+√2)=(x-(-√2)) then,

f(-√2) = 2×√2×(-√2)×(-√2) + 5×(-√2 )+ √2

= 4√2 - 5√2 + √2

= -√2 + √2

0

As , factor theorem states that if an expression f(x) is divided by (x- a) then, (x- a) will be the factor of f(x) iff f(a)=0.

Thus, by factor theorem, it's proved that (x+√2) is a factor of (2√2x^2 + 5x + √2)