Answer:
2(x + 2)² - 5
Explanation:
given
2x² + 8x + 3 ← factor out 2 from the first 2 terms
= 2(x² + 4x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 4x
= 2(x² + 2(2)x + 4 - 4) + 3
= 2(x + 2)² + 2(- 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5 ← in the form 2(x + p)² + q
with p = 2 and q = - 5