Answer:
The factorization of 2x² + 5x + 3 is (2x + 3)(x + 1)
Step-by-step explanation:
* Lets explain how to factor a trinomial in the form ax² ± bx ± c:
- Look at the c term first.
# If the c term is a positive number, then its factors r , s will both
be positive or both be negative it depends on the sign of b, if b
positive then both are positive if b negative then both are 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) where a = hk , c = rs and b = rk - hs
* Lets solve the problem
∵ The equation is 2x² + 5x + 3
∵ The general form of the trinomial is ax² + bx + c
∴ a = 2 , b = 5 , c = 6
∵ c is positive
∴ Its factors r and s have same sign
∵ a = 2
∵ The factors of a are h , k
∵ 2 = 2 × 1
∴ h = 2 and k = 1
∵ The factors of c are r , s
∵ 3 = 3 × 1
∴ r = 3 and s = 1
∵ The brackets are (hx + r)(kx - s)
∴ 2x² + 5x + 3 = (2x + 3)(x + 1)
∴ The factorization of 2x² + 5x + 3 is (2x + 3)(x + 1)
