Is this the correct way for a polynomial problem? Is it correct? Problem: Factor 4 5 2 + 4 x 4 5x 2 +4 completely. Step 1 Spot the pattern (quadratic in disguise). All the exponents are even, so let 2 y=x 2 . Now the polynomial becomes 2 5 + 4 y 2 5y+4. That's a regular quadratic. Step 2 Factor the quadratic in y. We need two numbers that multiply to + 4 +4 and add to 5 5. That's 4 4 and 1 1. So 2 5 + 4 ( 4 ) ( 1 ) y 2 5y+4=(y4)(y1). Step 3 Substitute back 2 y=x 2 . ( 4 ) ( 1 ) ( 2 4 ) ( 2 1 ) (y4)(y1)(x 2 4)(x 2 1). Step 4 Use difference of squares (twice). Each factor is a difference of squares: 2 4 ( 2 ) ( + 2 ) x 2 4=(x2)(x+2) and 2 1 ( 1 ) ( + 1 ) x 2 1=(x1)(x+1). Final answer (fully factored): 4 5 2 + 4 (