Answer:
2x² + 5x + 3 = (2x + 3)(x + 1)
Step-by-step explanation:
* Lets explain how to factor a trinomial in the form ax² ± bx ± c:
- Look at the last term c
# If the c term is a positive number, then its factors r , s will both
be positive or both be negative
# a has two factors h and k
# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs
# If the c term is a negative number, then either r or s will be negative,
but not both.
# a has two factors h and k
# The brackets are (hx + r)(kx - s) or (hx - r)(kx + s)where a = hk ,
c = rs and b = rk - hs
* Lets solve the problem
∵ The equation is 2x² + 5x + 3 = 0
∵ The general form of the equation is ax² + bx + c = 0
∴ a = 2 , b = 5 , c = 3
∵ c is positive
∴ Its factors r and s have same sign
∵ c = 3
∵ 3 = 3 × 1
∴ r = 3 and s = 1
∵ a = 2
∵ The factors of a are h , k
∵ 2 = 2 × 1
∴ h = 2 and k = 1
∵ The brackets are (hx + r)(kx + s)
∴ 2x² + 5x + 3 = (2x + 3)(x + 1)
